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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Name: ____________________   Date: ____________

1.Easy
0.7 kgk = ?

A 0.7 kg mass on a spring oscillates with a period of 0.35 s. Find the spring stiffness k.

m = 0.7 kgT = 0.35 s
k = N/m
2.Easy
1.5 kgk

A 1.5 kg mass on a spring makes 20 complete oscillations in 46 s. Find the frequency f of the oscillation.

m = 1.5 kgN = 20t = 46 s
f = Hz
3.Medium
t (s)x (cm)0.35 s

A 1.2 kg mass on a spring with k = 230 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.35 s (with sign).

m = 1.2 kgk = 230 N/mA = 6 cmt = 0.35 s
x = cm
4.Medium
3.1 kgk = 90 N/mA = 19 cmx = 4 cm

A 3.1 kg mass on a spring with k = 90 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 4 cm from equilibrium.

m = 3.1 kgk = 90 N/mA = 19 cmx = 4 cm
v = m/s
5.Hard
mk = 300 N/mA = 11 cmx = 4 cm

A mass on a spring with k = 300 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 300 N/mA = 11 cmx = 4 cm
U = J
6.Hard
0.2 kgk = 30 N/m

A 0.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 30 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.2 kgk = 30 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 225.6 N/m
  2. 2. f = 0.4348 Hz
  3. 3. x = 0.7965 cm
  4. 4. v = 1.001 m/s
  5. 5. U = 0.24 J
  6. 6. vmax = 0.801 m/s

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