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
3.9 kgk

A 3.9 kg mass on a spring makes 15 complete oscillations in 9 s. Find the frequency f of the oscillation.

m = 3.9 kgN = 15t = 9 s
f = Hz
2.Easy
3.5 kgk = ?

A 3.5 kg mass on a spring oscillates with a period of 1.55 s. Find the spring stiffness k.

m = 3.5 kgT = 1.55 s
k = N/m
3.Medium
t (s)x (cm)0.9 s

A 2.2 kg mass on a spring with k = 160 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 = 0.9 s (with sign).

m = 2.2 kgk = 160 N/mA = 11 cmt = 0.9 s
x = cm
4.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?14.25

A body oscillates in simple harmonic motion with period 1.2 s and amplitude 19 cm. What is the shortest time t it needs to move from its maximum displacement of 19 cm to a displacement of 14.25 cm?

T = 1.2 sA = 19 cmx = 14.25 cm
t = s
6.Hard
1 kgk = 250 N/mA = 9 cm

A 1 kg mass on a spring with k = 250 N/m is pulled 9 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 250 N/mA = 9 cm
amax = m/s²

Answer key

  1. 1. f = 1.667 Hz
  2. 2. k = 57.51 N/m
  3. 3. x = 1.956 cm
  4. 4. T = 3.108 s
  5. 5. t = 0.138 s
  6. 6. amax = 22.5 m/s²

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