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 kgk = ?24 cm

Hanging a 3 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 3 kgx = 24 cmg = 9.81 m/s²
k = N/m
2.Easy
3.4 kgk = 130 N/m

A 3.4 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.4 kgk = 130 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
4.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
5.Hard
2 kgk = 600 N/m500 m/s

A 15 g bullet moving at 500 m/s hits and stays in a 2 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 = 15 gv = 500 m/sM = 2 kgk = 600 N/m
A = cm
6.Hard
1.5 kgk = 380 N/m

A 1.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 380 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.5 kgk = 380 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 122.6 N/m
  2. 2. f = 0.9841 Hz
  3. 3. L = 0.994 m
  4. 4. T = 0.8971 s
  5. 5. A = 21.57 cm
  6. 6. vmax = 0.6163 m/s

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