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
1.7 kgk = 20 N/m

A 1.7 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 20 N/m
f = Hz
2.Easy
1.3 kgk = 70 N/m

A 1.3 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.3 kgk = 70 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
4.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
5.Hard
1.6 kgk = 300 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 300 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.6 kgk = 300 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
mk = 250 N/mA = 17 cmx = 4 cm

A mass on a spring with k = 250 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its kinetic energy K when it is 4 cm from equilibrium.

k = 250 N/mA = 17 cmx = 4 cm
K = J

Answer key

  1. 1. f = 0.5459 Hz
  2. 2. f = 1.168 Hz
  3. 3. L = 0.897 m
  4. 4. T = 3.357 s
  5. 5. vmax = 0.7164 m/s
  6. 6. K = 3.413 J

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