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
3.8 kgk = 90 N/m

A 3.8 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 90 N/m
T = s
2.Easy
1.6 kgk = 100 N/m

A 1.6 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 100 N/m
f = Hz
3.Medium
L = 1.4 mT = 3.85 s

An astronaut on another planet finds that a simple pendulum 1.4 m long has a period of 3.85 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.4 mT = 3.85 s
g = m/s²
4.Medium
0.8 kgk = 280 N/mA = 13 cmx = 12 cm

A 0.8 kg mass on a spring with k = 280 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 12 cm from equilibrium.

m = 0.8 kgk = 280 N/mA = 13 cmx = 12 cm
v = m/s
5.Hard
0.2 kgk = 240 N/m

A 0.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 240 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.2 kgk = 240 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1 kgk = 1200 N/m500 m/s

A 10 g bullet moving at 500 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 500 m/sM = 1 kgk = 1200 N/m
A = cm

Answer key

  1. 1. T = 1.291 s
  2. 2. f = 1.258 Hz
  3. 3. g = 3.729 m/s²
  4. 4. v = 0.9354 m/s
  5. 5. vmax = 0.2832 m/s
  6. 6. A = 14.36 cm

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