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
4 kgk

A 4 kg mass on a spring makes 50 complete oscillations in 25 s. Find the frequency f of the oscillation.

m = 4 kgN = 50t = 25 s
f = Hz
2.Easy
0.3 kgk = 120 N/m

A 0.3 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 0.3 kgk = 120 N/m
T = s
3.Medium
1.7 kgk = 320 N/mA = 9 cmx = 7 cm

A 1.7 kg mass on a spring with k = 320 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 = 1.7 kgk = 320 N/mA = 9 cmx = 7 cm
v = m/s
4.Medium
L = 0.5 mT = 1.33 s

An astronaut on another planet finds that a simple pendulum 0.5 m long has a period of 1.33 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.5 mT = 1.33 s
g = m/s²
5.Hard
0.5 kgk = 600 N/m500 m/s

A 10 g bullet moving at 500 m/s hits and stays in a 0.5 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 = 10 gv = 500 m/sM = 0.5 kgk = 600 N/m
A = cm
6.Hard
0.9 kgk = 490 N/mA = 10 cm

A 0.9 kg mass on a spring with k = 490 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.9 kgk = 490 N/mA = 10 cm
vmax = m/s

Answer key

  1. 1. f = 2 Hz
  2. 2. T = 0.3142 s
  3. 3. v = 0.7761 m/s
  4. 4. g = 11.16 m/s²
  5. 5. A = 28.58 cm
  6. 6. vmax = 2.333 m/s

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