Question 1

A block attached to a horizontal spring oscillates with a period $$T. If $$the mass of the block is doubled while the spring constant remains the same, what will be the new period of oscillation?

Accepted Answer

$$T_{new} = \sqrt{2}T$$

Question 2

A mass-spring system oscillates with a period $$T = 0.32\ 	ext{s}. If $$the amplitude of oscillation is doubled, what happens to the period?

Accepted Answer

The period remains the same.

Question 3

A pendulum clock is designed to have a period of $$2.00\ 	ext{s}. $$Using $$g = 9.81\ 	ext{m/s}^2$$, what should be the length of the pendulum?

Accepted Answer

$$0.99\ 	ext{m}$$

Question 4

Which equation correctly gives the period $$T of a $$mass $$m$$ attached to a spring with spring constant $$k$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 5

A block of mass $$0.50\ 	ext{kg}$$ attached to a spring oscillates with a period of $$0.32\ 	ext{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 192\ 	ext{N/m}$$

Question 6

If the acceleration due to gravity $$g$$ increases, what happens to the period of a simple pendulum of fixed length?

Accepted Answer

The period decreases.

Question 7

A block is released from rest at the amplitude of a horizontal spring-mass system. At what position is the kinetic energy of the block maximum?

Accepted Answer

At the equilibrium position.

Question 8

A mass-spring system oscillates with a period $$T. If $$the spring constant is quadrupled, what happens to the period?

Accepted Answer

The period is halved.

Question 9

A pendulum is moved from Earth to the Moon, where $$g is $$about $$1/6 of $$its value on Earth. How does the period change?

Accepted Answer

The period increases by a factor of $$\sqrt{6}.$$

Question 10

A block of mass $$m$$ attached to a spring is oscillating on a frictionless surface. If the total mechanical energy is $$E$$, what is the maximum speed $$v_{max} of $$the block?

Accepted Answer

$$v_{max} = \sqrt{\frac{2E}{m}}$$

Question 11

A mass-spring system is set into oscillation. Which of the following statements is true about the velocity and acceleration at the equilibrium position?

Accepted Answer

Velocity is maximum, acceleration is zero.

Question 12

A pendulum clock is running slow. Which adjustment will correct the timekeeping?

Accepted Answer

Shorten the length of the pendulum.

Question 13

A block of mass $$0.25\ 	ext{kg}$$ attached to a spring oscillates with a period of $$0.20\ 	ext{s}. $$What is the value of the spring constant $$k$$?

Accepted Answer

$$k = 246.7\ 	ext{N/m}$$

Question 14

Which of the following best describes the energy transformation in a mass-spring system at maximum displacement?

Accepted Answer

All energy is potential energy.

Question 15

A block attached to a spring is oscillating. If the block is replaced with a block of half the mass, what happens to the period?

Accepted Answer

The period decreases by a factor of $$\sqrt{2}.$$

Oscillations About Equilibrium: Examples and Applications

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