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
2.5 kgk = ?

A 2.5 kg mass on a spring oscillates with a period of 0.75 s. Find the spring stiffness k.

m = 2.5 kgT = 0.75 s
k = N/m
2.Easy
1.2 kgk = ?24.5 cm

Hanging a 1.2 kg mass on a spring stretches it by 24.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.2 kgx = 24.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
4.Medium
L = 0.7 mT = 2.73 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 2.73 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 2.73 s
g = m/s²
5.Hard
t (s)x (cm)t = ?12.8

A body oscillates in simple harmonic motion with period 3.4 s and amplitude 16 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12.8 cm?

T = 3.4 sA = 16 cmx = 12.8 cm
t = s
6.Hard
mk = 100 N/mA = 8 cmx = 1 cm

A mass on a spring with k = 100 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 100 N/mA = 8 cmx = 1 cm
K = J

Answer key

  1. 1. k = 175.5 N/m
  2. 2. k = 48.05 N/m
  3. 3. L = 0.2485 m
  4. 4. g = 3.708 m/s²
  5. 5. t = 0.5018 s
  6. 6. K = 0.315 J

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