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Periodic Motion

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?

Determining the Spring Constant K

A spring compressed by 0.080 meters stores 150 J as elastic potential energy. What is the value of the spring constant k? I need to see each step and formula to solve this question.

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

Optic Lasers

How many longitudinal modes can be obtained from a hypothetical laser with the gain profile allocated between the wavelengths of lambda = 630 and 640nm and having a resonator of 20cm length?

Period of a pendulum

See the attached file. Show all work. Explain how to find the exponent for a. (question b)

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

Harmonic Motion and Pendulum Clock

You are designing a pendulum clock to have a period of 1.0s. The acceleration of gravity is 9.81 m/s2. How long should the pendulum be in units of m?

Simple Harmonic Motion: Car on springs

The body of a 1261 kg car is supported on a frame by four springs. The spring constant of a single spring is 1.54 x 10 to the 4th N/m. Four people rinding in the car have a combined mass of 263 kg. When driven over a pothole in the road, the frame vibrates and for the first few seconds the vibration approximates simple harmon

Simple Harmonic motion problem..

A weight is suspended from a spring is seen to bob up and down over a distance of 30 cm twice each second. What is its frequency in Hz, period in units of s, and its amplitude in units of cm?

Show eqn E = 100 Sin(2(pi)x/3) Cos 5(pi)t is a mixture of 2

This question is from the text book 'OPTICS' fourth edition by Eugene Hecht. Thank you so much for your help. p.s I hope ,if possible, you could let me have answers as in pdf file or scaned paper(unless I could read or understand the letters that you wrote.. Cause, sometimes it's really hard to read the spelling in the se

Object Positioning

Simple Harmonic motion: Object moving in simple harmonic motion given by x = A cos (2*pi*ft.) has a frequency of 15.0 Hz and an amplitude of 8.0 mm. What is the position of the object at 0.05 s?

Determining the Wave Speed

If the distance between consecutive peaks of a wave is 4 meters, and if 40 peaks pass in a second, then how fast is the wave moving?

Refraction: Angle of Rays

At what angle must a ray be incident as it passes from a material which has index of refraction 1.41 to a material with index of refraction of 1.16. in order that the wave should remain in the original material?

Types of waves: Speed, frequency & wavelength

The speed of surface wave in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake with a speed of 2.0 m/s and a wavelength of 1.5 m. When these waves move into a shallower part of the lake their speed decreases to 1.6 m/s, though their frequency remains the same. Find the wavelengt

Periodic Motion of a Mass on a Spring

The position of a mass on a spring is given by x = (6.5 cm) cos [2 pi t/ (0.88s)]. (a) What is the period of this motion? (b) Where is the mass at t = 0.25 s? (c) Show that the mass is at the same location at 0.25 s + T seconds as it is at 0.25 s.