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
4 kgk = ?

A 4 kg mass on a spring makes 25 complete oscillations in 37 s. Find the spring stiffness k.

m = 4 kgN = 25t = 37 s
k = N/m
2.Easy
3.1 kgk = 240 N/m

A 3.1 kg mass on a spring with stiffness 240 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.1 kgk = 240 N/m
f = Hz
3.Medium
L = 1.2 mT = 3.57 s

An astronaut on another planet finds that a simple pendulum 1.2 m long has a period of 3.57 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.2 mT = 3.57 s
g = m/s²
4.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?3.6

A body oscillates in simple harmonic motion with period 3 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 3.6 cm?

T = 3 sA = 12 cmx = 3.6 cm
t = s
6.Hard
1.7 kgk = 120 N/mA = 12 cm

A 1.7 kg mass on a spring with k = 120 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.7 kgk = 120 N/mA = 12 cm
E = J

Answer key

  1. 1. k = 72.09 N/m
  2. 2. f = 1.4 Hz
  3. 3. g = 3.717 m/s²
  4. 4. T = 2.198 s
  5. 5. t = 0.6045 s
  6. 6. E = 0.864 J

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