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
4.1 kgk = 310 N/m

A 4.1 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 310 N/m
f = Hz
2.Easy
3.9 kgk = ?

A 3.9 kg mass on a spring oscillates with a period of 2.3 s. Find the spring stiffness k.

m = 3.9 kgT = 2.3 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)1.25 s

A 3.2 kg mass on a spring with k = 290 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.25 s (with sign).

m = 3.2 kgk = 290 N/mA = 14 cmt = 1.25 s
x = cm
5.Hard
mk = 400 N/mA = 13 cmx = 1 cm

A mass on a spring with k = 400 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 400 N/mA = 13 cmx = 1 cm
K = J
6.Hard
t (s)x (cm)t = ?7.2

A body oscillates in simple harmonic motion with period 0.4 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 7.2 cm?

T = 0.4 sA = 12 cmx = 7.2 cm
t = s

Answer key

  1. 1. f = 1.384 Hz
  2. 2. k = 29.11 N/m
  3. 3. L = 0.994 m
  4. 4. x = 11 cm
  5. 5. K = 3.36 J
  6. 6. t = 0.05903 s

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