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
0.3 kgk = 260 N/m

A 0.3 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.3 kgk = 260 N/m
f = Hz
2.Easy
3.6 kgk = 340 N/m

A 3.6 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.6 kgk = 340 N/m
f = Hz
3.Medium
2.7 kgk = 130 N/mA = 20 cmx = 10 cm

A 2.7 kg mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 10 cm from equilibrium.

m = 2.7 kgk = 130 N/mA = 20 cmx = 10 cm
v = m/s
4.Medium
L = 0.8 mT = 2.91 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 2.91 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 2.91 s
g = m/s²
5.Hard
1.3 kgk = 410 N/m

A 1.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 410 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.3 kgk = 410 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
2 kgk = 900 N/m200 m/s

An 8 g bullet moving at 200 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 = 900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 200 m/sM = 2 kgk = 900 N/m
A = cm

Answer key

  1. 1. f = 4.685 Hz
  2. 2. f = 1.547 Hz
  3. 3. v = 1.202 m/s
  4. 4. g = 3.73 m/s²
  5. 5. vmax = 0.5524 m/s
  6. 6. A = 3.764 cm

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