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 = ?

A 1.6 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 1.6 kgT = 0.7 s
k = N/m
2.Easy
4.7 kgk = 10 N/m

A 4.7 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 10 N/m
T = s
3.Medium
L = 3 m

A simple pendulum has a length of 3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 3 mg = 9.81 m/s²
T = s
4.Medium
3.7 kgk = 500 N/mA = 17 cmx = 15 cm

A 3.7 kg mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 15 cm from equilibrium.

m = 3.7 kgk = 500 N/mA = 17 cmx = 15 cm
v = m/s
5.Hard
3 kgk = 1200 N/m500 m/s

A 12 g bullet moving at 500 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 500 m/sM = 3 kgk = 1200 N/m
A = cm
6.Hard
mk = 20 N/mA = 15 cmx = 8 cm

A mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find the energy U stored in the spring when the mass is 8 cm from equilibrium.

k = 20 N/mA = 15 cmx = 8 cm
U = J

Answer key

  1. 1. k = 128.9 N/m
  2. 2. T = 4.308 s
  3. 3. T = 3.475 s
  4. 4. v = 0.93 m/s
  5. 5. A = 9.98 cm
  6. 6. U = 0.064 J

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