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
1.9 kgk = 270 N/m

A 1.9 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 1.9 kgk = 270 N/m
T = s
2.Easy
2 kgk = ?

A 2 kg mass on a spring oscillates with a period of 1.25 s. Find the spring stiffness k.

m = 2 kgT = 1.25 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
5.Hard
1.8 kgk = 330 N/mA = 5 cm

A 1.8 kg mass on a spring with k = 330 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.8 kgk = 330 N/mA = 5 cm
amax = m/s²
6.Hard
2.3 kgk = 440 N/m

A 2.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 440 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.3 kgk = 440 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.5271 s
  2. 2. k = 50.53 N/m
  3. 3. L = 0.6361 m
  4. 4. L = 0.159 m
  5. 5. amax = 9.167 m/s²
  6. 6. xmax = 10.26 cm

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