Q4. A particle moves anticlockwise on a circle of radius 4 cm with period 8 s, starting on the −x-axis. Write the x-projection and find it at t = 2 s.
ω = 2π/8 = π/4 rad/s and φ = π, so x = 4 cos(πt/4 + π) = −4 cos(πt/4) cm. At t = 2 s, x = −4 cos(π/2) = 0: the projection is passing the mean position.
Q5. The reference particle of an SHM moves at 2 m/s on a circle of radius 0.5 m. Find the amplitude, angular frequency and period of the SHM.
Amplitude = radius = 0.5 m. ω = v/A = 2/0.5 = 4 rad/s, so T = 2π/4 = π/2, about 1.57 s.
Q6. Why must sin(30°) and sin(30) be read differently?
An angle written without a unit is in radians. sin(30°) = 0.5, but sin(30) is the sine of 30 radians, about −0.988.