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 = 360 N/m

A 0.2 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 0.2 kgk = 360 N/m
T = s
2.Easy
1.7 kgk = ?

A 1.7 kg mass on a spring oscillates with a period of 1.2 s. Find the spring stiffness k.

m = 1.7 kgT = 1.2 s
k = N/m
3.Medium
t (s)x (cm)0.2 s

A 1.1 kg mass on a spring with k = 270 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.2 s (with sign).

m = 1.1 kgk = 270 N/mA = 14 cmt = 0.2 s
v = m/s
4.Medium
t (s)x (cm)0.15 s

A 1.4 kg mass on a spring with k = 350 N/m is pulled 8 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.15 s (with sign).

m = 1.4 kgk = 350 N/mA = 8 cmt = 0.15 s
v = m/s
5.Hard
mk = 200 N/mA = 15 cmx = 10 cm

A mass on a spring with k = 200 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its kinetic energy K when it is 10 cm from equilibrium.

k = 200 N/mA = 15 cmx = 10 cm
K = J
6.Hard
t (s)x (cm)t = ?2.4

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 2.4 cm?

T = 3.7 sA = 8 cmx = 2.4 cm
t = s

Answer key

  1. 1. T = 0.1481 s
  2. 2. k = 46.61 N/m
  3. 3. v = −0.01797 m/s
  4. 4. v = −0.8804 m/s
  5. 5. K = 1.25 J
  6. 6. t = 0.1794 s

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