oscillation of spring and vibration of tuning folk

See attached files for full problem description.

1. In a physics lab, you attach a 0.200 kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s.
a) Find the spring's force constant

2. A 42.5 kg chair is attached to a spring and allowed to oscillate. When the chair is empty the chair takes 1.30 s to make one complete vibration. But with a person sitting in it, with her feet off the floor, the chair now takes 2.54 s for one cycle.
what is the mass of the person?

3. A tuning fork labeled 392 Hz has the tip of each of the two prongs vibrating with amplitude of 0.600 mm.
a) What is the maximum speed of the tip of a prong?
b) A housefly with mass 0.0270 g is holding on to the tip of one of the prongs. As the prong vibrates, what is the fly's maximum kinetic energy? Assume the fly's mass has a negligible effect on the frequency of oscillation.

If a mass of 600.0 g is hung from the bottom of a vertical spring, the spring will stretch 28.0 cm. Now the hanging mass is removed, and the spring is placed horizontally on a frictionless table. One end of the spring is held fixed and the other end is attached to a 370.0 g mass. The mass is then pulled out a distance of 14.0 cm

Please see the attached file.
A weight of mass m is hung from the end of a spring which provides a restoring force equal to k times its extension. The weight is released from rest with the spring unextended. Find its position as a function of time, assuming negligible damping.

If the handle of a tuning fork is held solidly against a table, the sound from the tuning fork becomes louder. Why? How will this affect the length of time the fork keeps vibrating? Please explain.
This is a CONCEPTUAL question.

A 100 gram weight is hung from a spring with a spring constant of 10 N/m. the position of the mass is measured from he equilibrium point. The mass is pulled down 10 cm and released at T=0.
The position of the mass is given by x(t)=xcos(wt+theta).
What are the values of all the constants in this equation?
What is the maximum

1. A 300-g mass at the end of a spring oscillates with an amplitude of 7.0 cm and a frequency of 1.80 Hz. (a) Find its maximum speed and maximum acceleration. (b) What is its speed when it is 3.0 cm from its equilibrium position?
A) 8.96 m/s, 8.9 m/s2 (b) 0.45 m/s
B) 79.2 m/s, 895 m/s2 (b) 0.512 m/s
C) 0.79 m/s, 8

Please show the formula and work in following questions.
1. A pendulum is timed as it swings back and forth. The clock is started when the bob is at the left end of its swing. When the bob returns to the left end for the 90th return, the clock reads 60.0s.
a) What is the period of vibration?
b) What is the frequency of vibr

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If
the mass is displaced by 10 mm from its equilibrium position and
released, for the resulting vibration, calculate:
(a) (i) the frequency of vibration.
(ii) the maximum velocity of the mass during the vibration.
(iii) the maximum acceleration of the

A 0.50-kg mass is attached to a spring with a spring constant of 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

A 10.6 kg object oscillates at the end of a vertical spring that has a spring constant of 2.05 * 10^4 N/m. The effect of air resistance is represented by the damping coefficient b= 3.00 Ns/m. (a) Calculate the frequency of the damped oscillation. (b) By what percentage does the amplitude of the oscillation decrease in each cycl