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
3.3 kgk = ?

A 3.3 kg mass on a spring makes 40 complete oscillations in 18 s. Find the spring stiffness k.

m = 3.3 kgN = 40t = 18 s
k = N/m
2.Easy
2.2 kgk23 cm

Hanging a 2.2 kg mass on a spring stretches it by 23 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.2 kgx = 23 cmg = 9.81 m/s²
T = s
3.Medium
L = 1.5 mT = 2.58 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 2.58 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 2.58 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
5.Hard
2.6 kgk = 480 N/m

A 2.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 480 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.6 kgk = 480 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1.4 kgk = 150 N/mA = 10 cm

A 1.4 kg mass on a spring with k = 150 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.4 kgk = 150 N/mA = 10 cm
vmax = m/s

Answer key

  1. 1. k = 643.4 N/m
  2. 2. T = 0.9621 s
  3. 3. g = 8.896 m/s²
  4. 4. L = 0.994 m
  5. 5. vmax = 0.722 m/s
  6. 6. vmax = 1.035 m/s

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