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 0.9 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.9 kgk = 50 N/m

f = Hz

2.Easy

Hanging a 1.4 kg mass on a spring stretches it by 12 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 = 1.4 kgx = 12 cmg = 9.81 m/s²

T = s

3.Medium

A 1.7 kg mass on a spring with k = 240 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 6 cm from equilibrium.

m = 1.7 kgk = 240 N/mA = 9 cmx = 6 cm

v = m/s

4.Medium

A 2.7 kg mass on a spring with k = 260 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.25 s (with sign).

m = 2.7 kgk = 260 N/mA = 10 cmt = 1.25 s

v = m/s

5.Hard

A 20 g bullet moving at 100 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 3.5 kgk = 600 N/m

A = cm

6.Hard

A 1.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 280 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed v_max of the mass.

m = 1.5 kgk = 280 N/mg = 9.81 m/s²

v_max = m/s

Answer key

1. f = 1.186 Hz
2. T = 0.6949 s
3. v = 0.7971 m/s
4. v = 0.29 m/s
5. A = 4.352 cm
6. v_max = 0.718 m/s

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