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
4.2 kgk = 110 N/m

A 4.2 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.2 kgk = 110 N/m
f = Hz
2.Easy
0.2 kgk = 20 N/m

A 0.2 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.2 kgk = 20 N/m
f = Hz
3.Medium
2.6 kgk = 210 N/mA = 15 cmx = 8 cm

A 2.6 kg mass on a spring with k = 210 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its speed v when it is 8 cm from equilibrium.

m = 2.6 kgk = 210 N/mA = 15 cmx = 8 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
mk = 100 N/mA = 20 cmx = 11 cm

A mass on a spring with k = 100 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find the energy U stored in the spring when the mass is 11 cm from equilibrium.

k = 100 N/mA = 20 cmx = 11 cm
U = J
6.Hard
1.3 kgk = 380 N/m

A 1.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 380 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.3 kgk = 380 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 0.8145 Hz
  2. 2. f = 1.592 Hz
  3. 3. v = 1.14 m/s
  4. 4. T = 1.554 s
  5. 5. U = 0.605 J
  6. 6. xmax = 6.712 cm

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