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
3.7 kgk = 120 N/m

A 3.7 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 120 N/m
T = s
2.Easy
2.7 kgk = 10 N/m

A 2.7 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.7 kgk = 10 N/m
f = Hz
3.Medium
1.1 kgk = 60 N/mA = 15 cmx = 9 cm

A 1.1 kg mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its speed v when it is 9 cm from equilibrium.

m = 1.1 kgk = 60 N/mA = 15 cmx = 9 cm
v = m/s
4.Medium
L = 0.6 m

A simple pendulum has a length of 0.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.6 mg = 9.81 m/s²
T = s
5.Hard
1.8 kgk = 240 N/m

A 1.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 240 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.8 kgk = 240 N/mg = 9.81 m/s²
xmax = cm
6.Hard
mk = 260 N/mA = 15 cmx = 3 cm

A mass on a spring with k = 260 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 260 N/mA = 15 cmx = 3 cm
U = J

Answer key

  1. 1. T = 1.103 s
  2. 2. f = 0.3063 Hz
  3. 3. v = 0.8863 m/s
  4. 4. T = 1.554 s
  5. 5. xmax = 14.71 cm
  6. 6. U = 0.117 J

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