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
4.8 kgk = 50 N/m

A 4.8 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 50 N/m
T = s
2.Easy
2.5 kgk = ?

A 2.5 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 2.5 kgT = 0.65 s
k = N/m
3.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
4.Medium
L = 0.8 mT = 1.68 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 1.68 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 1.68 s
g = m/s²
5.Hard
3 kgk = 100 N/m500 m/s

A 12 g bullet moving at 500 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 500 m/sM = 3 kgk = 100 N/m
A = cm
6.Hard
t (s)x (cm)t = ?4.5

A body oscillates in simple harmonic motion with period 0.9 s and amplitude 9 cm. What is the shortest time t it needs to move from its maximum displacement of 9 cm to a displacement of 4.5 cm?

T = 0.9 sA = 9 cmx = 4.5 cm
t = s

Answer key

  1. 1. T = 1.947 s
  2. 2. k = 233.6 N/m
  3. 3. T = 3.357 s
  4. 4. g = 11.19 m/s²
  5. 5. A = 34.57 cm
  6. 6. t = 0.15 s

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