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
3.5 kgk = 350 N/m

A 3.5 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 350 N/m
T = s
2.Easy
1.5 kgk = ?

A 1.5 kg mass on a spring oscillates with a period of 0.45 s. Find the spring stiffness k.

m = 1.5 kgT = 0.45 s
k = N/m
3.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
1.2 kgk = 440 N/m

A 1.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 440 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.2 kgk = 440 N/mg = 9.81 m/s²
xmax = cm
6.Hard
mk = 80 N/mA = 4 cmx = 2 cm

A mass on a spring with k = 80 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its kinetic energy K when it is 2 cm from equilibrium.

k = 80 N/mA = 4 cmx = 2 cm
K = J

Answer key

  1. 1. T = 0.6283 s
  2. 2. k = 292.4 N/m
  3. 3. T = 0.8971 s
  4. 4. L = 1.68 m
  5. 5. xmax = 5.351 cm
  6. 6. K = 0.048 J

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