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
1.3 kgk = 380 N/m

A 1.3 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 380 N/m
T = s
2.Easy
2 kgk = 330 N/m

A 2 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 330 N/m
T = s
3.Medium
t (s)x (cm)0.35 s

A 4 kg mass on a spring with k = 20 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.35 s (with sign).

m = 4 kgk = 20 N/mA = 3 cmt = 0.35 s
v = m/s
4.Medium
t (s)x (cm)0.85 s

A 0.5 kg mass on a spring with k = 200 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.85 s (with sign).

m = 0.5 kgk = 200 N/mA = 13 cmt = 0.85 s
x = cm
5.Hard
0.2 kgk = 170 N/mA = 13 cm

A 0.2 kg mass on a spring with k = 170 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 170 N/mA = 13 cm
E = J
6.Hard
1.5 kgk = 230 N/mA = 13 cm

A 1.5 kg mass on a spring with k = 230 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 230 N/mA = 13 cm
E = J

Answer key

  1. 1. T = 0.3675 s
  2. 2. T = 0.4891 s
  3. 3. v = −0.0473 m/s
  4. 4. x = −3.577 cm
  5. 5. E = 1.437 J
  6. 6. E = 1.944 J

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