Simple Harmonic Motion

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Periodic motion is a type of motion that repeats itself after equal intervals of time. The smallest interval after which the motion repeats is called the time period (T). Example: motion of the hands …

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Oscillatory motion is a to-and-fro motion about a mean position. All oscillatory motions are periodic, but not all periodic motions are oscillatory. For example, the motion of Earth around the Sun is …

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Simple Harmonic Motion is a type of oscillatory motion where the acceleration of the particle is directly proportional to its displacement from the mean position and is always directed towards it. Mat…

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For a motion to be simple harmonic, the restoring force must be directly proportional to the displacement and opposite in direction: F = -kx. This leads to acceleration a = -(k/m)x = -ω²x.

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Given: A = 5 cm = 0.05 m, ω = 4 rad/s, φ = 0. Using: y(t) = A sin(ωt + φ) So, y(t) = 0.05 sin(4t) meters.

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Given: x = 4 sin(3t + π/6) cm → A = 4 cm = 0.04 m, ω = 3 rad/s Maximum velocity v_max = Aω = 0.04 × 3 = 0.12 m/s. Answer: 0.12 m/s.

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Formula: a_max = Aω² Given: a_max = 18 m/s², A = 0.06 m So, 18 = 0.06 × ω² → ω² = 18 / 0.06 = 300 → ω = √300 ≈ 17.32 rad/s. Answer: 17.32 rad/s.

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Formula: T = 2π√(l/g) Given: l = 1 m, g = 9.8 m/s² T = 2π√(1/9.8) = 2π√(0.102) ≈ 2π × 0.319 ≈ 2.00 s. Answer: 2.00 seconds.