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
2.5 kgk = ?

A 2.5 kg mass on a spring makes 15 complete oscillations in 18 s. Find the spring stiffness k.

m = 2.5 kgN = 15t = 18 s
k = N/m
2.Easy
2.3 kgk = ?

A 2.3 kg mass on a spring makes 40 complete oscillations in 53 s. Find the spring stiffness k.

m = 2.3 kgN = 40t = 53 s
k = N/m
3.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
4.Medium
L = 1.8 mT = 4.38 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 4.38 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 4.38 s
g = m/s²
5.Hard
0.7 kgk = 90 N/mA = 11 cm

A 0.7 kg mass on a spring with k = 90 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 90 N/mA = 11 cm
E = J
6.Hard
1.4 kgk = 120 N/mA = 5 cm

A 1.4 kg mass on a spring with k = 120 N/m is pulled 5 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.4 kgk = 120 N/mA = 5 cm
vmax = m/s

Answer key

  1. 1. k = 68.54 N/m
  2. 2. k = 51.72 N/m
  3. 3. T = 1.269 s
  4. 4. g = 3.704 m/s²
  5. 5. E = 0.5445 J
  6. 6. vmax = 0.4629 m/s

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