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
0.8 kgk = ?15 cm

Hanging a 0.8 kg mass on a spring stretches it by 15 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.8 kgx = 15 cmg = 9.81 m/s²
k = N/m
2.Easy
1.9 kgk = ?23.5 cm

Hanging a 1.9 kg mass on a spring stretches it by 23.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.9 kgx = 23.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
4.Medium
L = 0.6 mT = 1.63 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 1.63 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 1.63 s
g = m/s²
5.Hard
0.5 kgk = 380 N/mA = 7 cm

A 0.5 kg mass on a spring with k = 380 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.5 kgk = 380 N/mA = 7 cm
vmax = m/s
6.Hard
1.5 kgk = 1300 N/m400 m/s

A 10 g bullet moving at 400 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 400 m/sM = 1.5 kgk = 1300 N/m
A = cm

Answer key

  1. 1. k = 52.32 N/m
  2. 2. k = 79.31 N/m
  3. 3. T = 2.837 s
  4. 4. g = 8.915 m/s²
  5. 5. vmax = 1.93 m/s
  6. 6. A = 9.028 cm

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