Oscillation Problems
A machine part is undergoing simple harmonic motion with frequency f and amplitude A
on a flat surface. If the part is initially at x = 0 and moving in the negative x direction, it will be
at x = +A at time t equal to
A) 1/(2f)
B) 2f /3
C) 3/(4f)
D) 4f /3
A hollow thin-walled sphere of mass M and radius R can freely swing
about a pivot point on its surface. If it is displaced by a small amount from
its rest position, what is the square of its period of oscillation?
8 2 R
A)
3g
B)
20 R
3g
C)
R
8 2 R
D)
5g
28 R
5g
2
2
P
_____ A small leaf is floating on a lake’s surface. It is disturbed by a wave produced by a
passing motor boat. You can correctly infer that the leaf’s maximum speed
A) is opposite the wave’s propagation direction
B) occurs when its acceleration is zero
C) occurs at its maximum displacement
D) satisfies none of the above answers
A block attached to a spring is undergoing simple harmonic motion. What is the ratio of
its kinetic energy to its total mechanical energy when it is two-thirds of the way to the
maximum distance from its equilibrium position?
A) 2/3
B) 5/9
C) 1/3
D) 1/9
A quantity q(t) in a system satisfies the following equation: d2q/dt2 = −16q + 7q3. For
small displacements from its equilibrium position, what is the period of this quantity’s motion?
A) 2/π
B) ⅔π
C) ½π
y (m)
______ The figure at right shows a
snapshot taken at time t = 0 of a
continuous sinusoidal wave.
The
wave is known to be traveling to the
right. What is the frequency of the
wave (in Hz)?
A) 4
B) ½π
D) ⅛π
2
1
x (m)
1
C) ¼
2
3
4
5
6
7
8
D) More information needed
_____ A block attached to a spring performs a harmonic motion described by
x(t)=A cos(t +½). How was the oscillator initially set in motion at t=0?
A) By compressing the spring to x= A and then releasing it.
B) By pulling the spring to x=+A and then releasing it.
C) By giving the block a sharp hit when the spring is at its relaxed length.
D) By pulling the spring to x=A and then giving it a quick hit in the positive x-direction.
_____ An object undergoes simple harmonic motion described by x(t)=Acos(ωt+φ). When it was
released from rest at t=0, its x coordinate was negative. One correct value for the phase constant
φ is
B) π/4
A) 0
C) π/2
D) π
_____ A block is connected to a massless spring. The spring is initially stretched by a distance D
and then released to put the block into simple harmonic motion. By what distance is the spring
stretched when the spring potential energy equals the kinetic energy of the mass for the first
time after release?
A) ¼D
B) D/2
C) ½D
D) they are never equal
_____ The velocity of a block attached to a spring and undergoing simple harmonic motion in a
straight line is given by vx = 12 sin(4t–π/3), where t is time and all numbers are in appropriate SI
units. The amplitude of the oscillations is
A) ¾
B) 3
C) 12
D) 48
A massless rod of length L is rigidly connected at a right angle to the mid-point along one edge
of a uniform square of mass M and side length L. The other end of the rod is connected to a
pivot so that the system can oscillate freely as a physical pendulum. The period for small
oscillations about the pivot point is
A) 2𝜋√
11𝐿
18𝑔
B) 2𝜋√
11𝐿
12𝑔
C)
2𝜋
3
5𝐿
√𝑔
D)
2𝜋
3
𝐿
√𝑔
A block of mass M on a level frictionless surface is attached to a horizontal spring of force
constant k. It is oscillating with angular frequency ω and amplitude A. When the block has speed V,
half of the
total mechanical energy is kinetic. What is the position of the block?
A) A/√2
B) A/2
C) kV/M
D) MV/k
A uniform square plate with sides of length L is hanging from a frictionless
pivot P. If the plate is put into small oscillatory motion, what is its period?
A) 2𝜋√
5𝐿
12𝑔
B) 2𝜋√
5𝐿
6𝑔
C) 2𝜋√
6𝑔
5𝐿
D) √
6𝑔
5𝐿
P
L
L
A boy and a girl of the same weight are riding on a merry-go-round. The boy has more kinetic
energy than the girl. Who has the larger angular speed ω?
A) boy
B) girl
C) both have same ω
D) child farthest from center