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
3.2 kgk = 90 N/m

A 3.2 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.2 kgk = 90 N/m
f = Hz
2.Easy
4.2 kgk = 40 N/m

A 4.2 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 4.2 kgk = 40 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
4.Medium
0.7 kgk = 140 N/mA = 4 cmx = 3 cm

A 0.7 kg mass on a spring with k = 140 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 3 cm from equilibrium.

m = 0.7 kgk = 140 N/mA = 4 cmx = 3 cm
v = m/s
5.Hard
3 kgk = 600 N/m450 m/s

An 8 g bullet moving at 450 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 450 m/sM = 3 kgk = 600 N/m
A = cm
6.Hard
mk = 350 N/mA = 18 cmx = 3 cm

A mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 350 N/mA = 18 cmx = 3 cm
U = J

Answer key

  1. 1. f = 0.844 Hz
  2. 2. T = 2.036 s
  3. 3. L = 1.203 m
  4. 4. v = 0.3742 m/s
  5. 5. A = 8.474 cm
  6. 6. U = 0.1575 J

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