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 oscillates with a period of 0.4 s. Find the spring stiffness k.

m = 2 kgT = 0.4 s
k = N/m
2.Easy
1.5 kgk = ?

A 1.5 kg mass on a spring oscillates with a period of 1.2 s. Find the spring stiffness k.

m = 1.5 kgT = 1.2 s
k = N/m
3.Medium
2.5 kgk = 500 N/mA = 14 cmx = 12 cm

A 2.5 kg mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its speed v when it is 12 cm from equilibrium.

m = 2.5 kgk = 500 N/mA = 14 cmx = 12 cm
v = m/s
4.Medium
L = 1.7 mT = 4.25 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 4.25 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 4.25 s
g = m/s²
5.Hard
3.3 kgk = 140 N/mA = 19 cm

A 3.3 kg mass on a spring with k = 140 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.3 kgk = 140 N/mA = 19 cm
amax = m/s²
6.Hard
mk = 330 N/mA = 7 cmx = 5 cm

A mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find the energy U stored in the spring when the mass is 5 cm from equilibrium.

k = 330 N/mA = 7 cmx = 5 cm
U = J

Answer key

  1. 1. k = 493.5 N/m
  2. 2. k = 41.12 N/m
  3. 3. v = 1.02 m/s
  4. 4. g = 3.716 m/s²
  5. 5. amax = 8.061 m/s²
  6. 6. U = 0.4125 J

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