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
1.7 kgk = ?

A 1.7 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 1.7 kgT = 1 s
k = N/m
2.Easy
1.1 kgk

A 1.1 kg mass on a spring makes 30 complete oscillations in 53 s. Find the frequency f of the oscillation.

m = 1.1 kgN = 30t = 53 s
f = Hz
3.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.4 s

A 0.5 kg mass on a spring with k = 180 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.4 s (with sign).

m = 0.5 kgk = 180 N/mA = 9 cmt = 1.4 s
v = m/s
5.Hard
1 kgk = 420 N/mA = 19 cm

A 1 kg mass on a spring with k = 420 N/m is pulled 19 cm from equilibrium and released. Find its maximum speed vmax.

m = 1 kgk = 420 N/mA = 19 cm
vmax = m/s
6.Hard
1.8 kgk = 410 N/mA = 12 cm

A 1.8 kg mass on a spring with k = 410 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 410 N/mA = 12 cm
E = J

Answer key

  1. 1. k = 67.11 N/m
  2. 2. f = 0.566 Hz
  3. 3. T = 2.537 s
  4. 4. v = −1.691 m/s
  5. 5. vmax = 3.894 m/s
  6. 6. E = 2.952 J

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