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
1.6 kgk = 280 N/m

A 1.6 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 280 N/m
f = Hz
2.Easy
0.6 kgk = 310 N/m

A 0.6 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.6 kgk = 310 N/m
f = Hz
3.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
4.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
5.Hard
mk = 270 N/mA = 10 cmx = 8 cm

A mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its kinetic energy K when it is 8 cm from equilibrium.

k = 270 N/mA = 10 cmx = 8 cm
K = J
6.Hard
2 kgk = 240 N/m

A 2 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 speed vmax of the mass.

m = 2 kgk = 240 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. f = 2.105 Hz
  2. 2. f = 3.618 Hz
  3. 3. T = 2.691 s
  4. 4. T = 3.172 s
  5. 5. K = 0.486 J
  6. 6. vmax = 0.8955 m/s

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