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

A 3.3 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 350 N/m

T = s

2.Easy

Hanging a 1.6 kg mass on a spring stretches it by 19.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.6 kgx = 19.5 cmg = 9.81 m/s²

T = s

3.Medium

A 2.3 kg mass on a spring with k = 280 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 9 cm from equilibrium.

m = 2.3 kgk = 280 N/mA = 13 cmx = 9 cm

v = m/s

4.Medium

A 3.9 kg mass on a spring with k = 320 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.15 s (with sign).

m = 3.9 kgk = 320 N/mA = 4 cmt = 0.15 s

x = cm

5.Hard

A 12 g bullet moving at 200 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 = 12 gv = 200 m/sM = 0.5 kgk = 300 N/m

A = cm

6.Hard

A 15 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 = 1000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 300 m/sM = 0.5 kgk = 1000 N/m

A = cm

Answer key

1. T = 0.6101 s
2. T = 0.8859 s
3. v = 1.035 m/s
4. x = 0.8419 cm
5. A = 19.36 cm
6. A = 19.83 cm

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