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
2.3 kgk = 290 N/m

A 2.3 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 290 N/m
T = s
2.Easy
0.8 kgk = ?

A 0.8 kg mass on a spring makes 40 complete oscillations in 22 s. Find the spring stiffness k.

m = 0.8 kgN = 40t = 22 s
k = N/m
3.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
4.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
5.Hard
3 kgk = 1200 N/m200 m/s

A 15 g bullet moving at 200 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 = 15 gv = 200 m/sM = 3 kgk = 1200 N/m
A = cm
6.Hard
1.3 kgk = 100 N/mA = 2 cm

A 1.3 kg mass on a spring with k = 100 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.3 kgk = 100 N/mA = 2 cm
E = J

Answer key

  1. 1. T = 0.5596 s
  2. 2. k = 104.4 N/m
  3. 3. T = 2.104 s
  4. 4. T = 3.475 s
  5. 5. A = 4.988 cm
  6. 6. E = 0.02 J

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