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
2.8 kgk = 190 N/m

A 2.8 kg mass on a spring with stiffness 190 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.8 kgk = 190 N/m
f = Hz
2.Easy
1.5 kgk

A 1.5 kg mass on a spring makes 25 complete oscillations in 55 s. Find the frequency f of the oscillation.

m = 1.5 kgN = 25t = 55 s
f = Hz
3.Medium
L = 1.7 mT = 2.45 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 2.45 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 2.45 s
g = m/s²
4.Medium
0.5 kgk = 340 N/mA = 12 cmx = 2 cm

A 0.5 kg mass on a spring with k = 340 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 2 cm from equilibrium.

m = 0.5 kgk = 340 N/mA = 12 cmx = 2 cm
v = m/s
5.Hard
1.5 kgk = 1100 N/m300 m/s

A 5 g bullet moving at 300 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 300 m/sM = 1.5 kgk = 1100 N/m
A = cm
6.Hard
mk = 410 N/mA = 11 cmx = 1 cm

A mass on a spring with k = 410 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 410 N/mA = 11 cmx = 1 cm
K = J

Answer key

  1. 1. f = 1.311 Hz
  2. 2. f = 0.4545 Hz
  3. 3. g = 11.18 m/s²
  4. 4. v = 3.085 m/s
  5. 5. A = 3.687 cm
  6. 6. K = 2.46 J

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