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
2.1 kgk

A 2.1 kg mass on a spring makes 50 complete oscillations in 56 s. Find the frequency f of the oscillation.

m = 2.1 kgN = 50t = 56 s
f = Hz
2.Easy
2.9 kgk = ?10 cm

Hanging a 2.9 kg mass on a spring stretches it by 10 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.9 kgx = 10 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)0.35 s

A 0.4 kg mass on a spring with k = 270 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.35 s (with sign).

m = 0.4 kgk = 270 N/mA = 11 cmt = 0.35 s
x = cm
4.Medium
L = 1.4 mT = 3.86 s

An astronaut on another planet finds that a simple pendulum 1.4 m long has a period of 3.86 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.4 mT = 3.86 s
g = m/s²
5.Hard
1.6 kgk = 340 N/mA = 15 cm

A 1.6 kg mass on a spring with k = 340 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.6 kgk = 340 N/mA = 15 cm
vmax = m/s
6.Hard
3.3 kgk = 390 N/mA = 12 cm

A 3.3 kg mass on a spring with k = 390 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.3 kgk = 390 N/mA = 12 cm
E = J

Answer key

  1. 1. f = 0.8929 Hz
  2. 2. k = 284.5 N/m
  3. 3. x = −10.4 cm
  4. 4. g = 3.709 m/s²
  5. 5. vmax = 2.187 m/s
  6. 6. E = 2.808 J

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