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 = ?8.5 cm

Hanging a 2.5 kg mass on a spring stretches it by 8.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.5 kgx = 8.5 cmg = 9.81 m/s²
k = N/m
2.Easy
4.1 kgk = 220 N/m

A 4.1 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the period T.

m = 4.1 kgk = 220 N/m
T = s
3.Medium
L = 1.7 m

A simple pendulum has a length of 1.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.7 mg = 9.81 m/s²
T = s
4.Medium
L = 1 mT = 2.11 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 2.11 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 2.11 s
g = m/s²
5.Hard
t (s)x (cm)t = ?7

A body oscillates in simple harmonic motion with period 2.1 s and amplitude 10 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7 cm?

T = 2.1 sA = 10 cmx = 7 cm
t = s
6.Hard
2 kgk = 490 N/mA = 19 cm

A 2 kg mass on a spring with k = 490 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2 kgk = 490 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. k = 288.5 N/m
  2. 2. T = 0.8577 s
  3. 3. T = 2.616 s
  4. 4. g = 8.867 m/s²
  5. 5. t = 0.2592 s
  6. 6. amax = 46.55 m/s²

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