Physics 111 HW17
DUE Tuesday, 5 July 2016
M02. If an object on a horizontal frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced 0.120 m from its equilibrium position and released with zero initial speed, then after 0.800 s its displacement is found to be 0.120 m on the opposite side, and it has passed the equilibrium position once during this interval. Find the amplitude, period, and frequency.
M03. The displacement of an oscillating object as a function of time is shown in the figure at right. What is the frequency, amplitude, and period?
S01. A harmonic oscillator is made by using a 0.600 kg frictionless block and an ideal spring of unknown force constant. The oscillator is found to have a period of 0.150 s. Find the force constant of the spring.
S02. A 42.5-kg chair is attached to a spring and allowed to oscillate. When the chair is empty the chair takes 1.30s 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?
M04. A 2.00 kg mass executes simple harmonic oscillation with an amplitude of 5.00 cm. The maximum speed of the mass is 2.00 m/s.
a) Find the frequency of the oscillation in Hz.
b) If the mass is at x = 0m when t = 0s, find x(t).
M05. The motion of the piston of an automobile engine is approximately simple harmonic.
a) If the stroke of an engine (twice the amplitude) is 0.100 m and the engine runs at 3500 rev/min, compute the acceleration of the piston at the endpoint of its stroke.
b) If the piston has mass 0.450 kg, what net force must be exerted on it at this point?
S05. A 1.50 kg mass is attached to a spring (k = 200 N/m) and undergoes SHM going left and right on a frictionless horizontal table. The mass is in equilibrium at x = 0. The mass is released when t = 0s at coordinate x = 0.100m with a velocity of 2.00 m/s to the right. Find the constants A, ω, and δ in x(t) = A cos(ωt + δ).
S03. A 1.50-kg mass on a spring has displacement as a function of time given by the equation x(t) = (7.40 cm) cos[(4.16 s-1)t – 2.42]. Find
a) the time for one complete vibration;
b) the force constant of the spring;
c) the maximum speed of the mass;
d) the maximum force on the mass;
e) the position, speed, and acceleration of the mass at t = 1.00s, and the force on the mass at this time.
SP01. A 2 kg mass is hung from a 2 m long string tied to the ceiling. It is displaced an angle of 3o and let go at t = 0 so that it swings back and forth. Assume SHM (θ is small so that sinθ » θ).
a) Find the frequency of small oscillations of the mass as it swings back and forth.
b) Find the maximum speed of the mass using two methods:
i) Using conservation of energy, and
ii) taking the time derivative of θ(t).
SP03. You pull a simple pendulum of length 0.240 m to the side through an angle of 3.50o and release it.
a) How much time does it take the pendulum bob to reach its highest speed?
b) How much time does it take if the pendulum is released at an angle of 1.75o instead of 3.50o?
(over)