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
3 kgk = 340 N/m

A 3 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 3 kgk = 340 N/m
T = s
2.Easy
0.8 kgk = ?

A 0.8 kg mass on a spring makes 30 complete oscillations in 58 s. Find the spring stiffness k.

m = 0.8 kgN = 30t = 58 s
k = N/m
3.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
4.Medium
1.8 kgk = 110 N/mA = 6 cmx = 5 cm

A 1.8 kg mass on a spring with k = 110 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find its speed v when it is 5 cm from equilibrium.

m = 1.8 kgk = 110 N/mA = 6 cmx = 5 cm
v = m/s
5.Hard
0.5 kgk = 280 N/mA = 12 cm

A 0.5 kg mass on a spring with k = 280 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 280 N/mA = 12 cm
E = J
6.Hard
0.7 kgk = 330 N/m

A 0.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 330 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.7 kgk = 330 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.5902 s
  2. 2. k = 8.45 N/m
  3. 3. L = 0.159 m
  4. 4. v = 0.2593 m/s
  5. 5. E = 2.016 J
  6. 6. xmax = 4.162 cm

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