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 oscillates with a period of 1.05 s. Find the spring stiffness k.

m = 2.5 kgT = 1.05 s
k = N/m
2.Easy
2.3 kgk = 10 N/m

A 2.3 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 10 N/m
T = s
3.Medium
0.6 kgk = 210 N/mA = 18 cmx = 10 cm

A 0.6 kg mass on a spring with k = 210 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 10 cm from equilibrium.

m = 0.6 kgk = 210 N/mA = 18 cmx = 10 cm
v = m/s
4.Medium
L = 1.9 mT = 2.59 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 2.59 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 2.59 s
g = m/s²
5.Hard
2.5 kgk = 250 N/mA = 15 cm

A 2.5 kg mass on a spring with k = 250 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 250 N/mA = 15 cm
vmax = m/s
6.Hard
1 kgk = 80 N/mA = 20 cm

A 1 kg mass on a spring with k = 80 N/m is pulled 20 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 80 N/mA = 20 cm
amax = m/s²

Answer key

  1. 1. k = 89.52 N/m
  2. 2. T = 3.013 s
  3. 3. v = 2.8 m/s
  4. 4. g = 11.18 m/s²
  5. 5. vmax = 1.5 m/s
  6. 6. amax = 16 m/s²

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