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Simple Harmonic Motion
1. A spring is mounted in a linear oscillator. It is determined in this particular oscillator that a 4N force on the spring will cause a displacement of 0.02 meters.
A 2kg block is pulled a distance of 0.04 meters and then released, setting the system in
motion.
a. Find the spring constant.
b. Find the period and frequency of oscillation.
c. Calculate the maximum velocity attained.
d. Calculate the maximum acceleration.
e. Determine the total energy in the system.
f. Calculate the maximum potential energy.
g. Calculate the maximum kinetic energy.
2. Find the length of a simple pendulum whose period is 2.5 seconds on Earth.
3. A certain pendulum has a period of 2 seconds on Earth. What is its period on the surface of the moon (g =1/6th Earth)?
4. A simple linear oscillator is made of a 0.5 kg mass and a spring of unknown spring constant. It has a period of 0.2 seconds. Find the spring constant of the spring.
5. A block of unknown mass is attached to a spring with a constant of 200 N/m as a linear oscillator. It is found to have a frequency of 3Hz. Find the period, angular frequency and mass.
6. A block of mass 608 grams is fastened to a spring whose spring constant is 65 N/m. The block is pulled a distance of 11 cm from its equilibrium position and then released.
a. What force does the spring exert on the block just before the block is released?
b. What are the angular frequency, frequency and period?
c. What is the amplitude of oscillation?
d. What is the maximum speed of the block?
e. What is the magnitude of the maximum acceleration?
f. What is the total mechanical energy?
g. What is the potential energy when the displacement is halfway to the end point?
h. What is the kinetic energy at this point?
i. What is the speed at this point?
7. A body of mass 5 kg is suspended by a spring, which stretches 0.1 meters when the body is in equilibrium. The body is then displaced downward an additional 0.05 meters and released. Find the amplitude, period and frequency of the resulting motion.
8. x(t) = (0.21m)cos((10rad/s)t-1.33 rad) represents the position of a 4 kg oscillator.
a. Determine the maximum displacement of the oscillator.
b. Determine the magnitude of the maximum velocity.
c. Determine the magnitude of the maximum acceleration.
d. Determine the total energy of the oscillator.
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