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
3.7 kgk = ?

A 3.7 kg mass on a spring makes 30 complete oscillations in 41 s. Find the spring stiffness k.

m = 3.7 kgN = 30t = 41 s
k = N/m
2.Easy
1.3 kgk = ?

A 1.3 kg mass on a spring oscillates with a period of 1.75 s. Find the spring stiffness k.

m = 1.3 kgT = 1.75 s
k = N/m
3.Medium
L = 2.7 m

A simple pendulum has a length of 2.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.7 mg = 9.81 m/s²
T = s
4.Medium
L = 0.6 m

A simple pendulum has a length of 0.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.6 mg = 9.81 m/s²
T = s
5.Hard
2 kgk = 1600 N/m500 m/s

A 15 g bullet moving at 500 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 500 m/sM = 2 kgk = 1600 N/m
A = cm
6.Hard
2.5 kgk = 390 N/mA = 17 cm

A 2.5 kg mass on a spring with k = 390 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 390 N/mA = 17 cm
E = J

Answer key

  1. 1. k = 78.21 N/m
  2. 2. k = 16.76 N/m
  3. 3. T = 3.296 s
  4. 4. T = 1.554 s
  5. 5. A = 13.21 cm
  6. 6. E = 5.636 J

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