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
1.1 kgk = 180 N/m

A 1.1 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.1 kgk = 180 N/m
f = Hz
2.Easy
0.9 kgk

A 0.9 kg mass on a spring makes 10 complete oscillations in 5 s. Find the frequency f of the oscillation.

m = 0.9 kgN = 10t = 5 s
f = Hz
3.Medium
L = 2.1 m

A simple pendulum has a length of 2.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.1 mg = 9.81 m/s²
T = s
4.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
5.Hard
mk = 470 N/mA = 12 cmx = 9 cm

A mass on a spring with k = 470 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its kinetic energy K when it is 9 cm from equilibrium.

k = 470 N/mA = 12 cmx = 9 cm
K = J
6.Hard
0.5 kgk = 210 N/m

A 0.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 210 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.5 kgk = 210 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. f = 2.036 Hz
  2. 2. f = 2 Hz
  3. 3. T = 2.907 s
  4. 4. T = 2.457 s
  5. 5. K = 1.48 J
  6. 6. vmax = 0.4787 m/s

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