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
0.8 kgk = ?

A 0.8 kg mass on a spring oscillates with a period of 2.5 s. Find the spring stiffness k.

m = 0.8 kgT = 2.5 s
k = N/m
2.Easy
4.1 kgk = 260 N/m

A 4.1 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the period T.

m = 4.1 kgk = 260 N/m
T = s
3.Medium
L = 1.9 mT = 4.5 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 4.5 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 4.5 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.3 s? Use g = 9.81 m/s². Find L.

T = 1.3 sg = 9.81 m/s²
L = m
5.Hard
mk = 500 N/mA = 20 cmx = 2 cm

A mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 500 N/mA = 20 cmx = 2 cm
U = J
6.Hard
4 kgk = 400 N/mA = 10 cm

A 4 kg mass on a spring with k = 400 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 4 kgk = 400 N/mA = 10 cm
vmax = m/s

Answer key

  1. 1. k = 5.053 N/m
  2. 2. T = 0.789 s
  3. 3. g = 3.704 m/s²
  4. 4. L = 0.4199 m
  5. 5. U = 0.1 J
  6. 6. vmax = 1 m/s

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