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
1.6 kgk = 40 N/m

A 1.6 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 1.6 kgk = 40 N/m
T = s
2.Easy
0.7 kgk = ?

A 0.7 kg mass on a spring oscillates with a period of 1.5 s. Find the spring stiffness k.

m = 0.7 kgT = 1.5 s
k = N/m
3.Medium
0.2 kgk = 60 N/mA = 13 cmx = 4 cm

A 0.2 kg mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 4 cm from equilibrium.

m = 0.2 kgk = 60 N/mA = 13 cmx = 4 cm
v = m/s
4.Medium
1 kgk = 350 N/mA = 8 cmx = 7 cm

A 1 kg mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its speed v when it is 7 cm from equilibrium.

m = 1 kgk = 350 N/mA = 8 cmx = 7 cm
v = m/s
5.Hard
2.7 kgk = 210 N/m

A 2.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 210 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.7 kgk = 210 N/mg = 9.81 m/s²
xmax = cm
6.Hard
1.5 kgk = 230 N/mA = 19 cm

A 1.5 kg mass on a spring with k = 230 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.5 kgk = 230 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. T = 1.257 s
  2. 2. k = 12.28 N/m
  3. 3. v = 2.142 m/s
  4. 4. v = 0.7246 m/s
  5. 5. xmax = 25.23 cm
  6. 6. amax = 29.13 m/s²

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