# Worksheet: The Period of an Oscillating Spring

In this worksheet, we will practice analyzing the simple harmonic oscillations of objects attached to horizontally and vertically oscillating springs.

Q1:

A spring with a spring constant of 275 N/m suspends an object with an unknown mass. The object is pulled downward and then released, after which the suspended object oscillates. The frequency of the oscillation of the spring-and-object system is 1.45 Hz. What is the mass of the object suspended by the spring?

Q2:

A spring suspends an object with mass . The spring-and-object system oscillates with period . The object is replaced by an object with mass , and the period of oscillation of the spring-and-object system changes to . What is the ratio of to ?

Q3:

A spring suspends an object with a mass of 0.250 kg. The object is pulled downward and then released, after which the suspended spring-and-object system oscillates. The frequency of the oscillation of the spring-and-object system is 5.50 Hz. What is the spring constant?

• A217 N/m
• B54.3 N/m
• C13.6 N/m
• D267 N/m
• E299 N/m

Q4:

A spring suspends an object with a mass of 0.0150 kg. The object is pulled downward and then released, after which the suspended spring-and-object system oscillates. The period of the oscillation of the spring-and-object system is 0.0550 s. What is the spring constant of the spring?

• A196 N/m
• B2.94 N/m
• C62.3 N/m
• D19.5 N/m
• E438 N/m

Q5:

A spring suspends an object with mass . The spring-and-object system oscillates with period . The spring is then replaced by another spring with a spring constant of , and the period of oscillation of the spring-and-object system changes to . What is the ratio of to ?

Q6:

The graph shows the changes in the oscillation periods of five oscillating spring-and-object systems, where the masses of the objects are suspended by the springs. The springs all have different spring constants. Which color line represents the spring with the greatest spring constant? • AGreen
• BRed
• CBlack
• DBlue
• EOrange

Q7:

One end of a spring is attached to a fixed wall, and the other end of the spring is attached to a block, as shown in the diagram. The block rests on a smooth surface. The block is pulled to extend the spring and then released, and the spring-and-block system oscillates. The block is then brought to rest, returned to its initial position, and again pulled to extend the spring, but the new extension is greater than the extension that produced the original oscillations. The block is released, and the spring-and-block system oscillates. Which of the following statements about the oscillation period of the spring-and-block system for the two oscillation amplitudes is correct? • AThe period of oscillation of the spring-and-block system is smaller when the amplitude of the oscillations is greater.
• BThe period of oscillation of the spring-and-block system is greater when the amplitude of the oscillations is greater.
• CThe period of oscillation of the spring-and-block system is the same for both oscillation amplitudes.

Q8:

One end of a spring is attached to a fixed wall, and the other end of the spring is attached to a block, as shown in the diagram. The block rests on a smooth surface. The block is pulled to extend the spring and then released, and the spring-and-block system oscillates. The same spring and block are then used in a different configuration. The spring is suspended from a fixed platform and the block is initially supported to keep the spring at its unloaded equilibrium length. The block is then released, and the spring-and-block system oscillates. Which of the following statements about the oscillation period of the spring-and-block system in its two configurations is correct? The amplitude of oscillation is the same for both configurations. • AThe period of oscillation of the spring-and-block system is greater when the spring is vertically suspended.
• BThe period of oscillation of the spring-and-block system is the same in both configurations.
• CThe period of oscillation of the spring-and-block system is smaller when the spring is vertically suspended.

Q9:

A spring suspends an object with a mass of 0.250 kg. The spring constant of the spring is 150 N/m. The object is pulled downward and then released, after which the suspended spring-and-object system oscillates. What is the period of the oscillation of the spring-and-object system?

Q10:

A spring suspends an object with a mass of 0.15 kg. The spring constant of the spring is 120 N/m. The object is pulled downward and then released, after which the suspended spring-and-object system oscillates. What is the frequency of the oscillation of the spring-and-object system?

Q11:

Which of the following formulas correctly relates the period of an oscillating spring-and-object system to the mass of the object connected to the spring and the spring constant of the spring?

• A
• B
• C
• D
• E

Q12:

One end of a spring is attached to a fixed wall and the other end of the spring is attached to a block, as shown in the diagram. The block rests on a smooth surface. The block is pulled to extend the spring and then released, and the spring-and-block system oscillates. The mass of the block is 0.45 kg and the period of the oscillations is 0.60 s. The extension of the spring when the block is released is 0.15 m. What is the magnitude of the force from the spring that acts on the block when one of its vertical sides is at the equilibrium position of the center of the block? • A6.9 N
• B4.9 N
• C4.2 N
• D9.4 N
• E7.4 N

Q13:

The graph shows the changes in the oscillation periods of five oscillating spring-and-object systems with the masses of the objects suspended by the springs. The springs all have different spring constants. The spring constant of the spring represented by the orange line is 200 N/m and the spring constant of the spring represented by the blue line is 50 N/m. The difference in the period between each line and the line immediately adjacent to it on the graph is the same for the full range of mass values shown. What is the spring constant of the spring represented by the black line? Give your answer to three significant figures.

What is the spring constant of the spring represented by the red line? Give your answer to three significant figures.