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
5 kgk = 230 N/m

A 5 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 230 N/m
T = s
2.Easy
0.5 kgk = 360 N/m

A 0.5 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 360 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?14.25

A body oscillates in simple harmonic motion with period 3.3 s and amplitude 19 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 14.25 cm?

T = 3.3 sA = 19 cmx = 14.25 cm
t = s
6.Hard
1.2 kgk = 280 N/mA = 14 cm

A 1.2 kg mass on a spring with k = 280 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.2 kgk = 280 N/mA = 14 cm
vmax = m/s

Answer key

  1. 1. T = 0.9264 s
  2. 2. T = 0.2342 s
  3. 3. L = 1.431 m
  4. 4. L = 0.3578 m
  5. 5. t = 0.4454 s
  6. 6. vmax = 2.139 m/s

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