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
0.5 kgk = ?

A 0.5 kg mass on a spring oscillates with a period of 0.55 s. Find the spring stiffness k.

m = 0.5 kgT = 0.55 s
k = N/m
2.Easy
4.9 kgk = 140 N/m

A 4.9 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 140 N/m
T = s
3.Medium
2.1 kgk = 90 N/mA = 17 cmx = 2 cm

A 2.1 kg mass on a spring with k = 90 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 2 cm from equilibrium.

m = 2.1 kgk = 90 N/mA = 17 cmx = 2 cm
v = m/s
4.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
5.Hard
mk = 90 N/mA = 17 cmx = 12 cm

A mass on a spring with k = 90 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find the energy U stored in the spring when the mass is 12 cm from equilibrium.

k = 90 N/mA = 17 cmx = 12 cm
U = J
6.Hard
1.5 kgk = 100 N/m250 m/s

A 12 g bullet moving at 250 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 250 m/sM = 1.5 kgk = 100 N/m
A = cm

Answer key

  1. 1. k = 65.25 N/m
  2. 2. T = 1.175 s
  3. 3. v = 1.105 m/s
  4. 4. L = 0.6361 m
  5. 5. U = 0.648 J
  6. 6. A = 24.4 cm

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