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
3.7 kgk = 100 N/m

A 3.7 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 100 N/m
T = s
2.Easy
3.6 kgk = 200 N/m

A 3.6 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.6 kgk = 200 N/m
f = Hz
3.Medium
1.1 kgk = 460 N/mA = 6 cmx = 3 cm

A 1.1 kg mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find its speed v when it is 3 cm from equilibrium.

m = 1.1 kgk = 460 N/mA = 6 cmx = 3 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.5 s? Use g = 9.81 m/s². Find L.

T = 1.5 sg = 9.81 m/s²
L = m
5.Hard
0.2 kgk = 350 N/m

A 0.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 350 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.2 kgk = 350 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
2.7 kgk = 120 N/m

A 2.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 120 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.7 kgk = 120 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 1.209 s
  2. 2. f = 1.186 Hz
  3. 3. v = 1.063 m/s
  4. 4. L = 0.5591 m
  5. 5. vmax = 0.2345 m/s
  6. 6. vmax = 1.472 m/s

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