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
3.4 kgk = ?

A 3.4 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 3.4 kgT = 0.7 s
k = N/m
2.Easy
3.5 kgk = 350 N/m

A 3.5 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 350 N/m
T = s
3.Medium
t (s)x (cm)1.25 s

A 0.8 kg mass on a spring with k = 150 N/m is pulled 8 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.25 s (with sign).

m = 0.8 kgk = 150 N/mA = 8 cmt = 1.25 s
v = m/s
4.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
5.Hard
0.5 kgk = 240 N/mA = 13 cm

A 0.5 kg mass on a spring with k = 240 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.5 kgk = 240 N/mA = 13 cm
vmax = m/s
6.Hard
2.6 kgk = 140 N/mA = 8 cm

A 2.6 kg mass on a spring with k = 140 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.6 kgk = 140 N/mA = 8 cm
E = J

Answer key

  1. 1. k = 273.9 N/m
  2. 2. T = 0.6283 s
  3. 3. v = 1.081 m/s
  4. 4. L = 0.994 m
  5. 5. vmax = 2.848 m/s
  6. 6. E = 0.448 J

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