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 = ?

A 2.9 kg mass on a spring makes 50 complete oscillations in 33 s. Find the spring stiffness k.

m = 2.9 kgN = 50t = 33 s
k = N/m
2.Easy
4 kgk = ?

A 4 kg mass on a spring oscillates with a period of 0.95 s. Find the spring stiffness k.

m = 4 kgT = 0.95 s
k = N/m
3.Medium
t (s)x (cm)0.85 s

A 3.9 kg mass on a spring with k = 170 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.85 s (with sign).

m = 3.9 kgk = 170 N/mA = 12 cmt = 0.85 s
x = cm
4.Medium
L = 1.3 mT = 3.72 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 3.72 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 3.72 s
g = m/s²
5.Hard
1.5 kgk = 1200 N/m400 m/s

A 10 g bullet moving at 400 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 = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 400 m/sM = 1.5 kgk = 1200 N/m
A = cm
6.Hard
3.8 kgk = 120 N/mA = 19 cm

A 3.8 kg mass on a spring with k = 120 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.8 kgk = 120 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. k = 262.8 N/m
  2. 2. k = 175 N/m
  3. 3. x = 9.396 cm
  4. 4. g = 3.709 m/s²
  5. 5. A = 9.397 cm
  6. 6. amax = 6 m/s²

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