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
1.2 kgk = ?12 cm

Hanging a 1.2 kg mass on a spring stretches it by 12 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.2 kgx = 12 cmg = 9.81 m/s²
k = N/m
2.Easy
2.6 kgk = ?

A 2.6 kg mass on a spring oscillates with a period of 0.8 s. Find the spring stiffness k.

m = 2.6 kgT = 0.8 s
k = N/m
3.Medium
L = 1.8 mT = 2.83 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 2.83 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 2.83 s
g = m/s²
4.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
5.Hard
2 kgk = 220 N/mA = 4 cm

A 2 kg mass on a spring with k = 220 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 2 kgk = 220 N/mA = 4 cm
vmax = m/s
6.Hard
4 kgk = 1300 N/m200 m/s

An 8 g bullet moving at 200 m/s hits and stays in a 4 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 = 8 gv = 200 m/sM = 4 kgk = 1300 N/m
A = cm

Answer key

  1. 1. k = 98.1 N/m
  2. 2. k = 160.4 N/m
  3. 3. g = 8.873 m/s²
  4. 4. T = 2.457 s
  5. 5. vmax = 0.4195 m/s
  6. 6. A = 2.217 cm

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