A particle executes SHM along a straight line with mean position x = 0, period 20 s and amplitude 5 cm. The shortest time taken by the particle to go from x = 4 cm to x = -3 cm is:

• A. 4 s
• B. 7 s
• C. 5 s
• D. 6 s

To find the shortest time taken by a particle executing simple harmonic motion (SHM) to move from x = 4 cm to x = -3 cm, we first need to understand the motion parameters.

Key Parameters of SHM

• Mean Position (x₀): 0 cm
• Amplitude (A): 5 cm
• Period (T): 20 s

Position Function

The position of the particle in SHM can be described by the equation:

x(t) = A * cos(ωt), where ω = 2π/T.

Calculating ω:

ω = 2π/20 = π/10 rad/s.

Finding Time for Each Position

We need to find the times when the particle is at x = 4 cm and x = -3 cm.

For x = 4 cm:

4 = 5 * cos(ωt)

cos(ωt) = 4/5

ωt = cos^-1(4/5)

t₁ = (10/π) * cos^-1(4/5)

For x = -3 cm:

-3 = 5 * cos(ωt)

cos(ωt) = -3/5

ωt = cos^-1(-3/5)

t₂ = (10/π) * cos^-1(-3/5)

Calculating the Time Difference

The shortest time taken to move from x = 4 cm to x = -3 cm is:

Δt = t₂ - t₁.

Final Calculation

Using a calculator, we find:

Δt ≈ 6 s.

Thus, the shortest time taken by the particle to go from x = 4 cm to x = -3 cm is 6 s. Therefore, the correct answer is D. 6 s.