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 50 complete oscillations in 43 s. Find the frequency f of the oscillation.

m = 3.5 kgN = 50t = 43 s
f = Hz
2.Easy
3.1 kgk = ?

A 3.1 kg mass on a spring oscillates with a period of 1.4 s. Find the spring stiffness k.

m = 3.1 kgT = 1.4 s
k = N/m
3.Medium
L = 1.3 mT = 3.71 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 3.71 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 3.71 s
g = m/s²
4.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
5.Hard
t (s)x (cm)t = ?2.5

A body oscillates in simple harmonic motion with period 1.4 s and amplitude 5 cm. What is the shortest time t it needs to move from its maximum displacement of 5 cm to a displacement of 2.5 cm?

T = 1.4 sA = 5 cmx = 2.5 cm
t = s
6.Hard
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 1.4 s and amplitude 12 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 3 cm?

T = 1.4 sA = 12 cmx = 3 cm
t = s

Answer key

  1. 1. f = 1.163 Hz
  2. 2. k = 62.44 N/m
  3. 3. g = 3.729 m/s²
  4. 4. T = 2.537 s
  5. 5. t = 0.2333 s
  6. 6. t = 0.0563 s

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