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 kgk = ?

A 2 kg mass on a spring makes 10 complete oscillations in 30 s. Find the spring stiffness k.

m = 2 kgN = 10t = 30 s
k = N/m
2.Easy
0.7 kgk = 280 N/m

A 0.7 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 280 N/m
T = s
3.Medium
L = 0.7 mT = 4.13 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 4.13 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 4.13 s
g = m/s²
4.Medium
L = 0.8 mT = 1.68 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 1.68 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 1.68 s
g = m/s²
5.Hard
3.4 kgk = 220 N/mA = 2 cm

A 3.4 kg mass on a spring with k = 220 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.4 kgk = 220 N/mA = 2 cm
vmax = m/s
6.Hard
1.2 kgk = 450 N/mA = 14 cm

A 1.2 kg mass on a spring with k = 450 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.2 kgk = 450 N/mA = 14 cm
vmax = m/s

Answer key

  1. 1. k = 8.773 N/m
  2. 2. T = 0.3142 s
  3. 3. g = 1.62 m/s²
  4. 4. g = 11.19 m/s²
  5. 5. vmax = 0.1609 m/s
  6. 6. vmax = 2.711 m/s

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