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
2.9 kgk = 320 N/m

A 2.9 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.9 kgk = 320 N/m
f = Hz
2.Easy
3.7 kgk = 30 N/m

A 3.7 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 30 N/m
T = s
3.Medium
2.8 kgk = 330 N/mA = 9 cmx = 6 cm

A 2.8 kg mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 6 cm from equilibrium.

m = 2.8 kgk = 330 N/mA = 9 cmx = 6 cm
v = m/s
4.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
5.Hard
2.3 kgk = 120 N/mA = 5 cm

A 2.3 kg mass on a spring with k = 120 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 120 N/mA = 5 cm
amax = m/s²
6.Hard
2 kgk = 1900 N/m250 m/s

A 12 g bullet moving at 250 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 = 1900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 250 m/sM = 2 kgk = 1900 N/m
A = cm

Answer key

  1. 1. f = 1.672 Hz
  2. 2. T = 2.207 s
  3. 3. v = 0.7283 m/s
  4. 4. g = 8.821 m/s²
  5. 5. amax = 2.609 m/s²
  6. 6. A = 4.852 cm

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