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
3.8 kgk

A 3.8 kg mass on a spring makes 20 complete oscillations in 23 s. Find the frequency f of the oscillation.

m = 3.8 kgN = 20t = 23 s
f = Hz
2.Easy
0.2 kgk = ?

A 0.2 kg mass on a spring makes 50 complete oscillations in 15 s. Find the spring stiffness k.

m = 0.2 kgN = 50t = 15 s
k = N/m
3.Medium
t (s)x (cm)1 s

A 0.3 kg mass on a spring with k = 80 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1 s (with sign).

m = 0.3 kgk = 80 N/mA = 4 cmt = 1 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?3.2

A body oscillates in simple harmonic motion with period 1.6 s and amplitude 4 cm. What is the shortest time t it needs to move from its maximum displacement of 4 cm to a displacement of 3.2 cm?

T = 1.6 sA = 4 cmx = 3.2 cm
t = s
6.Hard
3.1 kgk = 130 N/mA = 11 cm

A 3.1 kg mass on a spring with k = 130 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.1 kgk = 130 N/mA = 11 cm
vmax = m/s

Answer key

  1. 1. f = 0.8696 Hz
  2. 2. k = 87.73 N/m
  3. 3. x = −3.251 cm
  4. 4. L = 0.897 m
  5. 5. t = 0.1639 s
  6. 6. vmax = 0.7123 m/s

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