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
3.3 kgk = 20 N/m

A 3.3 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 20 N/m
T = s
2.Easy
4.8 kgk = ?

A 4.8 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 4.8 kgT = 1.1 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
4.Medium
1.4 kgk = 380 N/mA = 13 cmx = 4 cm

A 1.4 kg mass on a spring with k = 380 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 4 cm from equilibrium.

m = 1.4 kgk = 380 N/mA = 13 cmx = 4 cm
v = m/s
5.Hard
t (s)x (cm)t = ?6

A body oscillates in simple harmonic motion with period 3.2 s and amplitude 20 cm. What is the shortest time t it needs to move from its maximum displacement of 20 cm to a displacement of 6 cm?

T = 3.2 sA = 20 cmx = 6 cm
t = s
6.Hard
mk = 350 N/mA = 17 cmx = 2 cm

A mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 350 N/mA = 17 cmx = 2 cm
U = J

Answer key

  1. 1. T = 2.552 s
  2. 2. k = 156.6 N/m
  3. 3. L = 0.8051 m
  4. 4. v = 2.038 m/s
  5. 5. t = 0.6448 s
  6. 6. U = 0.07 J

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