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
2.1 kgk

A 2.1 kg mass on a spring makes 40 complete oscillations in 30 s. Find the frequency f of the oscillation.

m = 2.1 kgN = 40t = 30 s
f = Hz
2.Easy
1.7 kgk = ?2 cm

Hanging a 1.7 kg mass on a spring stretches it by 2 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.7 kgx = 2 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.3 mT = 2.14 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 2.14 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 2.14 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
5.Hard
mk = 150 N/mA = 18 cmx = 13 cm

A mass on a spring with k = 150 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find the energy U stored in the spring when the mass is 13 cm from equilibrium.

k = 150 N/mA = 18 cmx = 13 cm
U = J
6.Hard
3.6 kgk = 490 N/mA = 2 cm

A 3.6 kg mass on a spring with k = 490 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.6 kgk = 490 N/mA = 2 cm
vmax = m/s

Answer key

  1. 1. f = 1.333 Hz
  2. 2. k = 833.8 N/m
  3. 3. g = 11.21 m/s²
  4. 4. L = 0.2013 m
  5. 5. U = 1.268 J
  6. 6. vmax = 0.2333 m/s

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