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
1.2 kgk = 370 N/m

A 1.2 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 1.2 kgk = 370 N/m
T = s
2.Easy
3.7 kgk = 250 N/m

A 3.7 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 250 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
4.Medium
L = 1.1 mT = 1.97 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.97 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.97 s
g = m/s²
5.Hard
3.8 kgk = 110 N/mA = 12 cm

A 3.8 kg mass on a spring with k = 110 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.8 kgk = 110 N/mA = 12 cm
amax = m/s²
6.Hard
1.6 kgk = 450 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 450 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.6 kgk = 450 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.3578 s
  2. 2. T = 0.7644 s
  3. 3. L = 0.2013 m
  4. 4. g = 11.19 m/s²
  5. 5. amax = 3.474 m/s²
  6. 6. vmax = 0.585 m/s

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