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
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 2.15 s. Find the spring stiffness k.

m = 0.2 kgT = 2.15 s
k = N/m
2.Easy
4.1 kgk = 180 N/m

A 4.1 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 180 N/m
f = Hz
3.Medium
L = 2 mT = 4.61 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 4.61 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 4.61 s
g = m/s²
4.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
5.Hard
t (s)x (cm)t = ?4.5

A body oscillates in simple harmonic motion with period 1.5 s and amplitude 18 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.5 cm?

T = 1.5 sA = 18 cmx = 4.5 cm
t = s
6.Hard
mk = 40 N/mA = 12 cmx = 9 cm

A mass on a spring with k = 40 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its kinetic energy K when it is 9 cm from equilibrium.

k = 40 N/mA = 12 cmx = 9 cm
K = J

Answer key

  1. 1. k = 1.708 N/m
  2. 2. f = 1.055 Hz
  3. 3. g = 3.715 m/s²
  4. 4. L = 0.2485 m
  5. 5. t = 0.06032 s
  6. 6. K = 0.126 J

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