If displacement in SHM is x(t) = A cos(ωt + φ), what is the expression for velocity v(t)?
A
v(t) = Aω cos(ωt + φ) B
v(t) = -Aω sin(ωt + φ) C
v(t) = A/ω sin(ωt + φ) D
v(t) = -A/ω cos(ωt + φ)
Analysis & Theory
Velocity is the derivative of displacement: v(t) = dx/dt = -Aω sin(ωt + φ).
What is the maximum velocity in SHM with amplitude A and angular frequency ω?
A
v_max = Aω B
v_max = A/ω C
v_max = A²ω D
v_max = ω/A
Analysis & Theory
The maximum value of velocity occurs when sin(ωt + φ) = ±1, so v_max = Aω.
At which position in SHM is the velocity maximum?
A
At the equilibrium position (x = 0) B
At maximum displacement (x = ±A) C
At half the amplitude (x = A/2) D
Velocity is constant everywhere
Analysis & Theory
Velocity is maximum when displacement is zero (equilibrium position).
At the extreme position of SHM (x = ±A), the velocity of the particle is:
A
Maximum B
Zero C
Equal to Aω D
Equal to -Aω
Analysis & Theory
At the extremes (x = ±A), the particle changes direction, so velocity is zero.
The relation between velocity v, displacement x, and amplitude A in SHM is:
A
v² = ω²(x² - A²) B
v² = ω²(A² - x²) C
v² = A² - ω²x² D
v² = ω²A² + x²
Analysis & Theory
From energy conservation in SHM: v² = ω²(A² - x²).