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
2.4 kgk = ?11.5 cm

Hanging a 2.4 kg mass on a spring stretches it by 11.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.4 kgx = 11.5 cmg = 9.81 m/s²
k = N/m
2.Easy
1.4 kgk = 360 N/m

A 1.4 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 1.4 kgk = 360 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
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
3 kgk = 500 N/m350 m/s

A 20 g bullet moving at 350 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 = 500 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 350 m/sM = 3 kgk = 500 N/m
A = cm
6.Hard
mk = 470 N/mA = 6 cmx = 4 cm

A mass on a spring with k = 470 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 470 N/mA = 6 cmx = 4 cm
U = J

Answer key

  1. 1. k = 204.7 N/m
  2. 2. T = 0.3918 s
  3. 3. L = 2.236 m
  4. 4. L = 0.6361 m
  5. 5. A = 18.01 cm
  6. 6. U = 0.376 J

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