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
4 kgk = ?

A 4 kg mass on a spring oscillates with a period of 0.8 s. Find the spring stiffness k.

m = 4 kgT = 0.8 s
k = N/m
2.Easy
4.6 kgk = 60 N/m

A 4.6 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the period T.

m = 4.6 kgk = 60 N/m
T = s
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
L = 1 mT = 4.94 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 4.94 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 4.94 s
g = m/s²
5.Hard
mk = 170 N/mA = 14 cmx = 5 cm

A mass on a spring with k = 170 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its kinetic energy K when it is 5 cm from equilibrium.

k = 170 N/mA = 14 cmx = 5 cm
K = J
6.Hard
1 kgk = 290 N/mA = 13 cm

A 1 kg mass on a spring with k = 290 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 1 kgk = 290 N/mA = 13 cm
vmax = m/s

Answer key

  1. 1. k = 246.7 N/m
  2. 2. T = 1.74 s
  3. 3. T = 1.099 s
  4. 4. g = 1.618 m/s²
  5. 5. K = 1.454 J
  6. 6. vmax = 2.214 m/s

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