simple harmonic motion
A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion of 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?
0.00 J
A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 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. At what distance from the equilibrium position are the kinetic and potential energy of the system the same?
0.17 m
A sewing machine needles moves in simple harmonic motion with a frequency of 2.5 Hz and and amplitude of 1.27cm a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? b) How long does it take the needle tip to travel a total distance of 11.43 cm?
0.20 seconds 0.90 seconds
If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?
0.25 Hz 4.0s
When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?
0.695 s
0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 570 N/m. The block is pulled from its equilibrium position at x= 0.0000 m to a displacement x=+0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is x=0.057 m, its kinetic energy is closest to
0.90 J
How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz?
1.00 kg
If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?
1.27 Hz
A leaky faucet drops 40 times in 30 seconds. What is the frequency of the dripping?
1.3 Hz
Spock has landed on a newly discovered planet and is instructed to determine its gravitational strength. He constructs a simple pendulum with a length of 700. mm and observes 20 full swings in 1 minute and 16.7 seconds. What does he deduce the "acceleration of gravity" to be from this?
1.88 m/s^2
An object is oscillating on a spring with a period of 4.60s. At time t=0.00 s the object has zero speed and is at x=8.30 cm. What is the acceleration of the object at t=2.50 s?
14.9 cm/s^2
If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?
2
A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?
24.1 N/m
A simple pendulum takes 2.00 seconds to make one complete swing. If we now triple the length, hw long will it take for one complete swing?
3.46 seconds
An astronaut has landed on Planet N-40 and conducts and experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0s. What is the acceleration of gravity on Planet N-40?
3.74 m/s^2
If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?
4
A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is 4.9 m, how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.
4.4 seconds
A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz a) What is the maximum speed of that point in SI units? b) What is the maximum acceleration of te point ins SI units?
6.82 m/s 3.75 x 10^4 m/s^2
A ball swinging at the end of a massless string, as shown in the figure, undergoes a simple harmonic motion. At what point or points is the magnitude of the instantaneous acceleration of the ball the greatest.
A and D
A simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?
Amplitude can not be determined from data given.
A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true?
Its elastic potential energy is zero, The acceleration is zero and the speed is zero.
A simple pendulum having a bob of pass M has a period T. If you double M but change nothing else, what would be the new period?
T
Two simple pendulums, A and B, are each 3.0m long, and the period of the pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?
T
If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true?
The angular frequency is doubled, the period is reduced to one-half of what it was
On the moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the moon?
T√ 6
In simple harmonic motion, when is its magnitude of acceleration is the greatest?
When the magnitude of the displacement is a maximum, when the kinetic energy is a minimum, and when the potential energy is a maximum
The total mechanical energy of a simple harmonic oscillating system is
a non-zero constant
A spring has 0.770 kg oscillating on it with a period of 1.25 seconds. a) what is the frequency? b) determine the spring constant c) if the mass is doubled and the spring was made 3 times stiffer, what is the new period?
a) 0.800 Hz b) 19.5 N/m c)1.02 s
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum?
at either A or B
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum.
at either A or B
A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the period of these two systems?
both periods would remain the same
When the mass of a simple pendulum is tripled, the time required for one complete vibration
does not change
An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could
double the force constant (spring constant) of the spring
An objected attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could
double the force constant (spring constant) of the spring
A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?
f
What is the frequency and period of a pendulum that makes 12 complete swings in 8.0 seconds?
frequency: 1.5 Hz time: 0.67 seconds
Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
increases the energy by a factor of two
A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true?
its acceleration is zero, its elastic potential energy is zero, its total mechanical energy is zero
Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate?
lower the weight
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum?
midway between A and B
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object when its kinetic energy is a maximum?
midway between A and B
Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g=1.6m/s^2, and set into oscillation. Which of the following statements about these systems are true?
on the moon, ball B will take longer to complete once cycle than ball A on the moon, ball A will execute more vibrations each minute than ball B
Doubling only the amplitude of a vibrating mass-on-a-spring system produces what effect on the system frequency?
produces no change
The total energy stored in simple harmonic motion of a mass-spring system is proportional to the
square of amplitude
If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true?
the angular frequency is doubled, the period is reduced to one-half of what it was
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into free fall?
the period becomes infinite because the pendulum would not swing
A pendulum of length L is suspended from the ceilings of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?
the period increases
In simple harmonic motion, when is the speed the greatest?
when the magnitude of the acceleration is a minimum, when the potential energy is zero
In a simple harmonic motion, when is the magnitude of the acceleration the greatest?
when the magnitude of the displacement is a maximum, when the potential energy is a maximum, when the kinetic is a minimum