Suppose you were to increase the spring constant of a spring by a factor of 4 without changing the mass of the attached block or amplitude of its oscillation. How would the maximum speed of the block be affected?
It would increase by a factor of 2
Consider four different systems, each made of a block attached to an ideal horizontal spring. Rank them in order of their total mechanical energy, from largest to smallest value.
(a) Block mass 0.50 kg and spring constant 500 N/m, with amplitude 0.020 m.
(b) Block mass 0.60 kg and spring constant 300 N/m, with speed 1.0 m/s when passing through equilibrium.
(c) Block mass 1.2 kg and spring constant 400 N/m, with speed 0.50 m/s when passing through x=−0.010 m.
(d) Block mass 2.0 kg and spring constant 200 N/m, with speed 0.20 m/s when passing through x=0.050 m.
(b), (d), (c), (a)
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A small object is attached to a horizontal spring, pushed to position x=−A, and released. The object in the resulting simple harmonic motion oscillates with period T.
How long does it take for the object to travel a total distance of 3A?
3T/4
A block attached at the end of a spring undergoes simple harmonic motion with frequency of oscillation ω.
Which of the following modifications will make the block oscillate with a greater frequency?
Increase the spring constant
A simple harmonic oscillator completes 1420 cycles in 20.0 min.
Calculate the period of the motion.
T=(20.0min/1420cycles)×(60s/1min)=0.845s
A simple harmonic oscillator completes 1420 cycles in 20.0 min, with T = 0.845s.
Calculate the frequency of the motion.
f=1/T=1/0.845s=1.18Hz
What is the mass of an object that is attached to a spring with a force constant of 220 N/m if 14 oscillations occur each 16 s? (Express your answer to two significant figures.)
m=k(T/2π)^2=27.3kg
A block is attached to a horizontal spring, the spring stretched so the block is located at x=A, and released.
At what point in the resulting simple harmonic motion is the speed of the block at its maximum?
x=0
A block is attached to a horizontal spring, the spring stretched so the block is located at x=A, and released.
At what point in the resulting simple harmonic motion is the magnitude of the acceleration of the block at its maximum?
x=A and x=−A
A small object is attached to a horizontal spring, pushed to position x=−A, and released.
In one full cycle of its motion, the total distance traveled by the object is
4A
A small object is attached to a horizontal spring and set in simple harmonic motion with amplitude A and period T.
How long does it take for the object to travel a total distance of 6A?
3T/2
An object-spring system undergoes simple harmonic motion.
If the amplitude increases but the mass of the object is not changed, the total energy of the system
increases
You can double the maximum speed of a simple harmonic oscillator by?
*doubling the amplitude.
*reducing the mass to one-fourth its original value.
*increasing the spring constant to four times its original value.
Replacing an object on a spring with an object having one quarter the original mass will have the result of changing the frequency of the vibrating spring by a factor of
2
A box of mass 8 kg slides across a frictionless surface at an initial speed 1.5 m/s into a relaxed spring of spring constant 69 N/m.
How long is the box in contact with the spring before it bounces off in the opposite direction?
tcontact =
1.07s
High tide occurs at 8:00 A.M. and is 1 m above sea level. Six hours later, low tide is 1 m below sea level. After another 6 h, high tide occurs (again 1 m above sea level), then finally one last low tide (6 h later, 1 m below sea level).
Write a mathematical expression that would predict the level of the ocean at this beach at any time of day.
x=(1m)cos((2π/12h)t−4π/3)
An object on a spring slides on a horizontal frictionless surface with simple harmonic motion. Assume the maximum displacement of the object is A so that it oscillates between +A and -A.
Determine where the object’s kinetic energy and potential energy are the same.
±A/√2
The potential energy of an object on a spring is 2.4 J at a location where the kinetic energy is 1.6 J. The amplitude of the simple harmonic motion is 28 cm.
Calculate the spring constant. (Express your answer to two significant figures.)
k=(2(Uspring+K))/A^2
=(2((2.4J)+(1.6J)))/(0.28m)^2
=100N/m
The potential energy of an object on a spring is 2.4 J at a location where the kinetic energy is 1.6 J. The amplitude of the simple harmonic motion is 28 cm. k=100N/m.
Find the largest force that the object experiences. (Express your answer to two significant figures.)
Fmax=kA
=(100Nm)(0.28m)
=29N
The potential energy of a simple harmonic oscillator is given by U=1/2kx^2, x(t)=Acos(vt).
Choose the correct expression for the velocity, v(t).
v(t)=−wAsin(wt)
The sounds made by male mosquitoes in flight are close to 650 Hz, while those made by females are close to 400 Hz. The antenae of mosquitoes differ from male to female. The natural frequency of a male’s antennae is about 400 Hz, while that of the female’s is about 200 Hz. Biologists suspect that some mosquitoes can detect the presence of others based on nerve signals generated when their antennae vibrate. Would you expect that…
Males can detect females
A small marble is attached to a thread that has negligible mass and is hung from a support. When the marble is pulled back a small distance and released, it swings in simple harmonic motion with a frequency of f. What is the frequency of the pendulum after the length of the thread is increased by a factor of 4, but the marble is still released in the same way?
f/2
Geoff counts the number of oscillations of a simple pendulum at a location where the acceleration due to gravity is 9.80 m/s^2, and finds that it takes 22.0 s for 12 complete cycles.
Calculate the length of the pendulum. (Express your answer to three significant figures.)
L=g(T/2π)^2
=0.834m
A uniform rod of length L hangs from one end and oscillates with a small amplitude. The moment of inertia for a rod rotating about one end is I=(1/3)ML^2.
What is the period of the rod’s oscillation?
2π(√(2L/3g))
If the period of a simple pendulum is T and we increase its length so that it’s four times longer.
What will the new period be?
2T
A 550-g object is attached to a spring with a force constant of 2.20 N/m. The object rests on a horizontal surface that has a viscous, oily substance spread evenly on it. The object is pulled 12.0 cm to the right of the equilibrium position and set into harmonic motion. After 3.00 s, the amplitude has fallen to 7.00 cm due to frictional losses in the oil.
Calculate the natural frequency of the system. (Express your answer to three significant figures.)
ω0=√k/m
=√(2.2N/m)/0.550kg
=2rads
