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
1.1 kgk = 350 N/m

A 1.1 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 1.1 kgk = 350 N/m
T = s
2.Easy
3.1 kgk = ?

A 3.1 kg mass on a spring makes 30 complete oscillations in 55 s. Find the spring stiffness k.

m = 3.1 kgN = 30t = 55 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.1 mT = 1.32 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.32 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.32 s
g = m/s²
5.Hard
t (s)x (cm)t = ?6

A body oscillates in simple harmonic motion with period 1 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6 cm?

T = 1 sA = 8 cmx = 6 cm
t = s
6.Hard
2.5 kgk = 310 N/mA = 12 cm

A 2.5 kg mass on a spring with k = 310 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.5 kgk = 310 N/mA = 12 cm
amax = m/s²

Answer key

  1. 1. T = 0.3522 s
  2. 2. k = 36.41 N/m
  3. 3. L = 0.159 m
  4. 4. g = 24.92 m/s²
  5. 5. t = 0.135 s
  6. 6. amax = 14.88 m/s²

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