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
1.5 kgk = ?8 cm

Hanging a 1.5 kg mass on a spring stretches it by 8 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.5 kgx = 8 cmg = 9.81 m/s²
k = N/m
2.Easy
4.7 kgk = 80 N/m

A 4.7 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 80 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
4.Medium
L = 0.9 mT = 4.68 s

An astronaut on another planet finds that a simple pendulum 0.9 m long has a period of 4.68 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.9 mT = 4.68 s
g = m/s²
5.Hard
2.7 kgk = 270 N/mA = 7 cm

A 2.7 kg mass on a spring with k = 270 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.7 kgk = 270 N/mA = 7 cm
amax = m/s²
6.Hard
t (s)x (cm)t = ?4.75

A body oscillates in simple harmonic motion with period 1 s and amplitude 19 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.75 cm?

T = 1 sA = 19 cmx = 4.75 cm
t = s

Answer key

  1. 1. k = 183.9 N/m
  2. 2. T = 1.523 s
  3. 3. L = 2.236 m
  4. 4. g = 1.622 m/s²
  5. 5. amax = 7 m/s²
  6. 6. t = 0.04022 s

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