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
0.9 kgk

A 0.9 kg mass on a spring makes 10 complete oscillations in 16 s. Find the frequency f of the oscillation.

m = 0.9 kgN = 10t = 16 s
f = Hz
2.Easy
1.4 kgk

A 1.4 kg mass on a spring makes 25 complete oscillations in 30 s. Find the frequency f of the oscillation.

m = 1.4 kgN = 25t = 30 s
f = Hz
3.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
4.Medium
2.4 kgk = 410 N/mA = 11 cmx = 10 cm

A 2.4 kg mass on a spring with k = 410 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 10 cm from equilibrium.

m = 2.4 kgk = 410 N/mA = 11 cmx = 10 cm
v = m/s
5.Hard
2.2 kgk = 480 N/mA = 15 cm

A 2.2 kg mass on a spring with k = 480 N/m is pulled 15 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.2 kgk = 480 N/mA = 15 cm
E = J
6.Hard
0.7 kgk = 40 N/m

A 0.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 40 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.7 kgk = 40 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 0.625 Hz
  2. 2. f = 0.8333 Hz
  3. 3. T = 2.198 s
  4. 4. v = 0.599 m/s
  5. 5. E = 5.4 J
  6. 6. xmax = 34.34 cm

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