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
0.8 kgk = 280 N/m

A 0.8 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 280 N/m
T = s
2.Easy
2.4 kgk = 130 N/m

A 2.4 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the period T.

m = 2.4 kgk = 130 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.65 s

A 2.6 kg mass on a spring with k = 50 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.65 s (with sign).

m = 2.6 kgk = 50 N/mA = 12 cmt = 0.65 s
v = m/s
5.Hard
1.2 kgk = 450 N/mA = 4 cm

A 1.2 kg mass on a spring with k = 450 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.2 kgk = 450 N/mA = 4 cm
E = J
6.Hard
t (s)x (cm)t = ?12

A body oscillates in simple harmonic motion with period 0.5 s and amplitude 20 cm. What is the shortest time t it needs to move from its maximum displacement of 20 cm to a displacement of 12 cm?

T = 0.5 sA = 20 cmx = 12 cm
t = s

Answer key

  1. 1. T = 0.3359 s
  2. 2. T = 0.8537 s
  3. 3. L = 0.6361 m
  4. 4. v = −0.1511 m/s
  5. 5. E = 0.36 J
  6. 6. t = 0.07379 s

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