Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

Hanging a 0.2 kg mass on a spring stretches it by 19 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.2 kgx = 19 cmg = 9.81 m/s²

k = N/m

2.Easy

A 0.8 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 400 N/m

T = s

3.Medium

A 2.9 kg mass on a spring with k = 400 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.95 s (with sign).

m = 2.9 kgk = 400 N/mA = 11 cmt = 0.95 s

v = m/s

4.Medium

A 3.2 kg mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 1 cm from equilibrium.

m = 3.2 kgk = 330 N/mA = 7 cmx = 1 cm

v = m/s

5.Hard

A 5 g bullet moving at 300 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 300 m/sM = 0.5 kgk = 300 N/m

A = cm

6.Hard

A 12 g bullet moving at 400 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 400 m/sM = 4 kgk = 400 N/m

A = cm

Answer key

1. k = 10.33 N/m
2. T = 0.281 s
3. v = 1.275 m/s
4. v = 0.7036 m/s
5. A = 12.19 cm
6. A = 11.98 cm

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