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
2.1 kgk = 270 N/m

A 2.1 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 270 N/m
T = s
2.Easy
3.5 kgk = 130 N/m

A 3.5 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 130 N/m
T = s
3.Medium
3.1 kgk = 340 N/mA = 14 cmx = 4 cm

A 3.1 kg mass on a spring with k = 340 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its speed v when it is 4 cm from equilibrium.

m = 3.1 kgk = 340 N/mA = 14 cmx = 4 cm
v = m/s
4.Medium
L = 1.7 mT = 1.65 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 1.65 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 1.65 s
g = m/s²
5.Hard
3.8 kgk = 130 N/mA = 9 cm

A 3.8 kg mass on a spring with k = 130 N/m is pulled 9 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.8 kgk = 130 N/mA = 9 cm
amax = m/s²
6.Hard
mk = 20 N/mA = 4 cmx = 3 cm

A mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its kinetic energy K when it is 3 cm from equilibrium.

k = 20 N/mA = 4 cmx = 3 cm
K = J

Answer key

  1. 1. T = 0.5541 s
  2. 2. T = 1.031 s
  3. 3. v = 1.405 m/s
  4. 4. g = 24.65 m/s²
  5. 5. amax = 3.079 m/s²
  6. 6. K = 0.007 J

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