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
3.2 kgk = ?

A 3.2 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 3.2 kgT = 0.65 s
k = N/m
2.Easy
4 kgk = ?

A 4 kg mass on a spring makes 30 complete oscillations in 9 s. Find the spring stiffness k.

m = 4 kgN = 30t = 9 s
k = N/m
3.Medium
L = 2.6 m

A simple pendulum has a length of 2.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.6 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
1.6 kgk = 180 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 180 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.6 kgk = 180 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
mk = 370 N/mA = 16 cmx = 7 cm

A mass on a spring with k = 370 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find the energy U stored in the spring when the mass is 7 cm from equilibrium.

k = 370 N/mA = 16 cmx = 7 cm
U = J

Answer key

  1. 1. k = 299 N/m
  2. 2. k = 1755 N/m
  3. 3. T = 3.235 s
  4. 4. L = 0.8051 m
  5. 5. vmax = 0.9249 m/s
  6. 6. U = 0.9065 J

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