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
0.8 kgk = 100 N/m

A 0.8 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.8 kgk = 100 N/m
f = Hz
2.Easy
3 kgk

A 3 kg mass on a spring makes 20 complete oscillations in 48 s. Find the frequency f of the oscillation.

m = 3 kgN = 20t = 48 s
f = Hz
3.Medium
L = 0.7 mT = 1.77 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 1.77 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 1.77 s
g = m/s²
4.Medium
0.8 kgk = 310 N/mA = 9 cmx = 7 cm

A 0.8 kg mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 7 cm from equilibrium.

m = 0.8 kgk = 310 N/mA = 9 cmx = 7 cm
v = m/s
5.Hard
2.5 kgk = 230 N/mA = 12 cm

A 2.5 kg mass on a spring with k = 230 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 230 N/mA = 12 cm
E = J
6.Hard
3 kgk = 200 N/m200 m/s

A 20 g bullet moving at 200 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 = 200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 3 kgk = 200 N/m
A = cm

Answer key

  1. 1. f = 1.779 Hz
  2. 2. f = 0.4167 Hz
  3. 3. g = 8.821 m/s²
  4. 4. v = 1.114 m/s
  5. 5. E = 1.656 J
  6. 6. A = 16.28 cm

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