Explore BrainMass

Periodic Motion

Period motion is repeated motion at equal intervals of time. There are many different examples of periodic motion being performed, a bounding call, vibrating tuning fork, a rocking chair or a water wave. The interval for a single repetition or cycle is called a period. The number of periods per unit of time is called its frequency. For example, a period of the Earth’s orbit is one year and its frequency is one orbit per year.

Period= 1/frequency

Frequency= 1/period

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The phenomena of simple harmonic motion can be seen in the motion of a simple pendulum and molecular vibration. The equation of the restoring force, F, can be seen in the following equation:

F= -kx

Where k is the spring constant and x is the displacement from the equilibrium.
The sinusoidal function of a simple harmonic motion can be solved using a differential equation

x(t)= c_1 cos(ωt)+ c_2 sin(ωt)=Acos(ωt- φ)


ω= √(k/m)

A= √(c_1^2+c_2^2 )

tan〖φ= c_2/c_1 〗

Where c_1 and c_2 are constants that can be solved for.

Physics: Kinematic Problems

1. A bead slides without friction around a loop-the-loop. The bead is released from a height of 8.5 m from the bottom of the loop-the-loop which has a radius 3 m.The acceleration of gravity is 9.8 m/s. What speed is it at point a? 2. A bobsled slides down an ice track starting (at zero initial speed) from the top of a(n) 171

Simple Pendulum Gravity

Simple Pendulum Gravity is responsible for an object falling toward Earth. The farther the object falls, the faster it is moving when it hits the ground. For each second that an object falls, its speed increases by a constant amount, called the acceleration due to gravity, denoted g. One way to calculate the value of g is to use

Simple pendulum equations

Simple Pendulum Gravity is responsible for an object falling toward Earth. The farther the object falls, the faster it is moving when it hits the ground. For each second that an object falls, its speed increases by a constant amount, called the acceleration due to gravity, denoted g. One way to calculate the value of g is to use

Mechanics, damped linear pendulum

The equation of motion for a damped linear pendulum is (d^2?/dt^2)+2?(d?/dt)+Ï?^2?=0 where Ï?=sqrt(l/g) and ? are positive constants, with l the length of the pendulum and g gravity. If l=1, g=9.81 and ?=1/4 and ?(0)=3, how long does it take the pendulum swinging from rest to reach the position ?=0. How long does it take to

Wave length and amplitude

A wave on a string is described by the following equation (assume the +x direction is to the right). y = (11 cm) cos[πx/(4.4 cm) + π t/(12 s)] (a) What is the amplitude of this wave? _______cm (b) What is its wavelength? _______cm (c) What is its period? _______ s (d) What is its speed? _______cm/s (e) In which di

distance up the incline after launched by a spring

Please see the attachment for full description and figure The spring shown in Figure P11.54 is compressed 40 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30° incline is 0.15. (a) What is the student's speed j

Simple Harmonic Motion: Position, velocity, and energy

A block of mass m is attached to a spring whose spring constant is k. The other end of the spring is fixed so that when the spring is unstretched, the mass is located at x=0. Assume that the +x direction is to the right. The mass is now pulled to the right a distance A beyond the equilibrium position and released, at time t=0

Pepe and Alfredo are resting on an offshore raft after a swim.

Pepe and Alfredo are resting on an offshore raft after a swim. They estimate that 3.0 m separates a trough and an adjacent crest of surface waves on the lake. They count 15 crests that pass by the raft in 19.5 s. Calculate how fast the waves are moving. [I tried saying that frequency= 15/19.5=.769 V=f(3) =(.769)(3)

Loss of energy as a child goes to and fro on a swing

According to the principle of conservation of energy, when a child plays on a swing the potential energy he possesses at the top of his path is converted to kinetic energy as he falls and back to potential energy as he swings up on the other side. According to this description, a child should be able to swing indefinitely withou

Change in Period or Amplitude of an Undamped Oscillator

An undamped oscillator has a period t_o = 1.000 s, but I now add a little damping so that its period changes to t_1 = 1.001 s. What is the damping factor B? By what factor will the amplitude of oscillation decrease after 10 cycles? What effect of damping would be more noticeable, the change of period or the decrease of amplitude

Matrix Representation: Hamiltonian of the Infinite Square Well

Consider the eigenstates of the infinite square well defined by V(x<-a/2) = infinity V(-a/2 < x < a/2) = 0 V (x> a/s) = infinity a. If the Hilbert space base-kets for this potential are seen in the attachment. Write down the matrix representation for the Hamiltonian H-hat of the system. b. What is the matrix representati

Simple Harmonic Oscillations: Springs with Masses

Show that the values of w^2 (omega^2) for the three simple harmonic oscillations (a), (b), (c) in the diagram (Attached) are in the ratio 1:2:4. I said for a) that w^2 = s/2m (since the spring stiffness intuitively I think must be 1/2 less than just a single spring) b) w^2 = s/m c) w^2 = 2s/m Which gives a ratio of 0

Involving Hamiltonian Dynamics

Involving Hamiltonian Dynamics problem 5.6 A mass m is suspended by a massless spring of spring constant k and unstretched length b. The suspension point has a constant upward acceleration a(0 subscript of a). Gravity is acting vertically downward. Find the Lagrangian and Hamiltonian functions and obtain Hamilton's equation

Finding the Speed, Frequency and Period of Tsunami Waves

Please help with the following problem. Provide step by step calculations. Tsunamis are fast-moving waves generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching the shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the

Nature of waves

A person lying on an air mattress in the ocean rises and falls through one complete cycle every 5.5 seconds. The crests of the wave causing the motion are 21.0 m apart. (a) Determine the frequency of the wave. (b) Determine the speed of the wave.


A wave causes a displacement y that is given in meters according to y=(0.45) sin (8.0 * 3.14t - 3.14x), where t and x are expressed in seconds and meters. a.) What is the amplitude of the wave? b.) what is the frequency of the wave? c.) What is the wavelength of the wave? d.) What is the speed of the wave? e.) Is th

Density of Water and Oil

A certain object weighs 100 N. When placed in water it weighs 72 N and when placed in oil it weighs 82 N. a) What is the density of the object? b) What is the density of the oil?

Oscillations and Waves

Groundhogs know physics!! They ventilate their burrows by building a mound over one entrance, which is open to a stream of air; and the other entrance is at ground level that is open to stagnant air. How exactly does this construction ventilate the burrow?

Standing Wave and Harmonic Motions

A tube of air is open at only one end and has a length of 1.5 m. This tube sustains a standing wave at its third harmonic. What is the distance between one node and the adjacent antinode?

Eigen frequencies of the coupled oscillators

3 Oscillators of equal mass are coupled such that the potential energy of the system is given by: U = 1/2[k1*(x1^2+x3^2)+k2*x2^2 +k3(x1*x2+x2*x3)] and k3=(2*k1*k2)^1/2 Find the eigen frequencies by solving the secular equation. What does the zero -frequency mode mean?

Time period of particle in a hole along diameter of earth.

1. A hole is drilled straight through the center of the earth and a particle is dropped into the hole. Neglect rotational effects: a) Show that the particle's motion is simple harmonic motion. b) Calculate the Period of oscillation. 2. If a field vector is independent of the radial distance within a sphere, find the

Phase Space and Phase Diagram in Mechanics

Please provide a clear detailed explanation (with examples) of the meaning and calculation of phase space and phase diagram. Also solve the following problem: A mass m moves in one dimension and is subjected to a constant force +F1 when x<0 and to a constant force -F1 when x>0. Find the following: a) construct a ph

The apparent frequency of waves and the speed of waves.

A jet skier is moving at 8.4 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.2hz, and the crests are separated by 5.8m. What is the wave speed?

Spring Constant of Springs

A 50 g mass hanger hangs moitionless from a partially stretched spring. When a 80 gram mass is added to the hanger, the spring stretch increases by 8 cm. What is the spring constant of the spring (in N/m)? (Assume g = 9.79 m/s2.)

Periodic Motion: Moment of Inertia

A 1.80-kg connecting rod from a car engine is pivoted about a horizontal knife edge as shown in the figure above. The center of gravity of the rod was located by balancing and is 0.200 m from the pivot. When it is set into small amplitude oscillation, the rod makes 100 complete swings in 120 s. Calculate the moment of inertia

Simple Harmonic Motion: Block-spring system.

(See attached file for full problem description) --- Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun; an

A pendulum with a wooden rod and steel disc blade swings in small oscillations and at the same time the whole system moves down. To determine number of oscillations of the pendulum when it has moved down by 1m.

A torture technique used by inquisition included a pendulum with attached blade. The length and mass of the wooden rod are L=5m and M=10kg, and the steel disk blade has m=30kg and radius R=30cm. While the pendulum swings, the whole system moves vertically down at a rate of 1mm/min. Considering that the pendulum has a small amp

Simple Harmonic Motion:Oscillation of 2 blocks with 3 spring

The word document has a graph that is necessary to understand the problem, please go directly there. A harmonic force [F0 sin wt)] is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 be the deviations from equilibrium for m1 and m2, respectively. Ignore gravity. 1) Wr

Undamped Coupled Oscillators

Undamped coupled oscillators: Two identical undamped oscillators, A and B, each of mass m and natural frequency &#969;_0 are coupled in such a way that the coupling force exerted on A is &#963;m(d^2x_b/dt^2), and the coupling force exerted on B is &#963;m(d^2x_a/dt^2), where &#963; is a coupling constant of magnitude less tha