displacement
In simple harmonic motion, the restoring force must be proportional to the
the acceleration varies sinusoidally with time
An oscillatory motion must be simple harmonic if
proportional to the displacement
In simple harmonic motion, the magnitude of the acceleration is
0.7T
A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. Of the following times, at which time is it furthest from the equilibrium point?
it is at x = 0 and is traveling toward x = +xm
A particle moves back and forth along the x axis from x = -xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T
in equilibrium at the center of its path because the acceleration is zero there
A particle oscillating in simple harmonic motion is
has varying acceleration
An object is undergoing simple harmonic motion. Throughout a complete cycle it
none of these
When a body executes simple harmonic motion, its acceleration at the ends of its path must be
none of the above
A particle is in simple harmonic motion with period T. At time t = 0 it is halfway between the equilibrium point and an end point of its motion, traveling toward the end point. The next time it is at the same place is
0.50s
An object attached to one end of a spring makes 20 complete oscillations in 10 s. Its period is
2 Hz
An object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is
12.6 rad/s
An object attached to one end of a spring makes 20 vibrations in 10 s. Its angular frequency is
f = w/2π
Frequency f and angular frequency w are related by
20cm, 4Hz
A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10cm and x = 5ocm and it goes from one of these extremes to the other in 0.25s. Its amplitude and frequency are
T
A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be
the displacement is maximum
In simple harmonic motion, the magnitude of the acceleration is greatest when
velocity is zero
In simple harmonic motion, the displacement is maximum when the
the acceleration is greatest at the maximum displacement
In simple harmonic motion
both the initial displacement and velocity
The amplitude and phase constant of an oscillator are determined by
They are started so the combination (w^2)(x0^2) + (vo^2) is the same
Two identical undamped oscillators have the same amplitude of oscillation only if
doubling both initial displacement and the initial speed
The amplitude of any oscillator can be doubled by
periods
It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different
π/2 rad
The acceleration of a body executing simple harmonic motion leads the velocity by what phase?
π/2 rad
The displacement of an object oscillating on a spring is given by x(t)=xmcos(wt+φ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant φ is
π/2 and π rad
The displacement of an object oscillating on a spring is given by x(t)=xmcos(wt+φ). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant φ is between
is 33 rad/s
A certain spring elongates 9.0mm when it is suspended vertically and a block of mass M is hung on it. The natural angular frequency of this block-spring system
A√(k/m)
An object of mass m, oscillating on the end of a spring with constant k, has amplitude A. Its maximum speed is
0.10m
A 0.20-kg object attached to a spring whose constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is
T/√2
Ch 15 #29
A simple harmonic oscillator consists of a particle of mass m and an ideal spring with with constant k. Particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be
100
A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds. Its maximum velocity in m/s is
7500 N/m
A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2cos(50t) where x is in meters and t is in seconds. The spring constant of the spring is
Kavg = Uavg
Let U bet the potential energy (with zero at zero displacement) and K be the kinetic energy of a simple harmonic oscillator. Uavg and Kavg are the average values over a cycle. Then
K = 0 and U = 8J
A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. At one point in its motion its kinetic energy is K = 5J and its potential energy (measured with U=0 at x=0) is U = 3J. When it is at x = xm, the kinetic and potential energies are
K = 5J and U = 3J
A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. At one point in its motion its kinetic energy is K = 5J and its potential energy (measured with U=0 at x=0) is U = 3J. When it is at x = -(1/2)x1, the kinetic and potential energies are
0.24m
A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0J, then the amplitude of the oscillation is
6.9 m/s
A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0J, then the maximum speed of the block is
5.2 m/s
A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is
0.18m
A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is
both the amplitude and the maximum are twice as great
An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial
37.5J
A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface. Its total energy is 50J. When the displacement is half the amplitude, the kinetic energy is
±A/√2
A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is
be greater by a factor of √2
If the length of a simple pendulum is doubled, its period will
√10 s
The period of a simple pendulum is 1s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes
4
The amplitude of oscillation of a simple pendulum is increased from 1˚ to 4˚. Its maximum acceleration changes by a factor of
decrease its length to L/4
A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f
none of the above
A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension force of the string is
none of these
A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its midpoint. The period then becomes
2π√(L/(g+a))
A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is
all the same
Three physical pendulums, with masses m1, m2=2m1, and m3=3m1, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest
5, 4, 3, 2, 1
Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are
hoop 1: M=150g and R=50cm
hoop 2: M=200g and R=40cm
hoop 3: M=250g and R=30cm
hoop 4: M=300g and R=20cm
hoop 5: M=350g and R=10cm
Order the hoops according to the periods of their motions, smallest to largest
hoop 1: M=150g and R=50cm
hoop 2: M=200g and R=40cm
hoop 3: M=250g and R=30cm
hoop 4: M=300g and R=20cm
hoop 5: M=350g and R=10cm
Order the hoops according to the periods of their motions, smallest to largest
a = 0.3 m
A meter stick is pivoted at a point on a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?
67 cm
The rotational inertia of a uniform thin rod about its end is ML^2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0m this rod will have the same period as a simple pendulum of the length
the larger radius
Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces. The one with the longer period of oscillation is the one with
the amplitudes and frequencies are both the same
The x and y coordinates of a point each execute simple harmonic motion. The result might be a circular orbit if
an ellipse
The x and y coordinates of a point each execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be
none of the above is true
For an oscillator subjected to a damping force proportional to its velocity
k = 150 N/m, m = 50g, b = 5 g/s
Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?
the same as the natural frequency of the oscillator
A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be
the damping force
A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by
its amplitude is constant
An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time
the applied force
A block on a spring is subjected to a damping force that is proportional to its velocity and to an applied sinusoidal force. The energy dissipated by damping is supplied by
E
Ch 15 #62
The table below gives the values of the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of these takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?
