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
4.9 kgk = 190 N/m

A 4.9 kg mass on a spring with stiffness 190 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 190 N/m
T = s
2.Easy
2.7 kgk = 330 N/m

A 2.7 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.7 kgk = 330 N/m
f = Hz
3.Medium
L = 0.6 mT = 2.52 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 2.52 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 2.52 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?4.2

A body oscillates in simple harmonic motion with period 2.4 s and amplitude 7 cm. What is the shortest time t it needs to move from its maximum displacement of 7 cm to a displacement of 4.2 cm?

T = 2.4 sA = 7 cmx = 4.2 cm
t = s
6.Hard
mk = 170 N/mA = 5 cmx = 2 cm

A mass on a spring with k = 170 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 170 N/mA = 5 cmx = 2 cm
U = J

Answer key

  1. 1. T = 1.009 s
  2. 2. f = 1.76 Hz
  3. 3. g = 3.73 m/s²
  4. 4. L = 2.09 m
  5. 5. t = 0.3542 s
  6. 6. U = 0.034 J

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