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
3.5 kgk

A 3.5 kg mass on a spring makes 20 complete oscillations in 58 s. Find the frequency f of the oscillation.

m = 3.5 kgN = 20t = 58 s
f = Hz
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 2.45 s. Find the spring stiffness k.

m = 5 kgT = 2.45 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
5.Hard
1.1 kgk = 140 N/mA = 14 cm

A 1.1 kg mass on a spring with k = 140 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.1 kgk = 140 N/mA = 14 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?7.5

A body oscillates in simple harmonic motion with period 0.4 s and amplitude 10 cm. What is the shortest time t it needs to move from its maximum displacement of 10 cm to a displacement of 7.5 cm?

T = 0.4 sA = 10 cmx = 7.5 cm
t = s

Answer key

  1. 1. f = 0.3448 Hz
  2. 2. k = 32.88 N/m
  3. 3. L = 0.159 m
  4. 4. T = 3.357 s
  5. 5. vmax = 1.579 m/s
  6. 6. t = 0.04601 s

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