The displacement of a particle in SHM varies according to the relation x =4(Cos πt + Sin πt). The amplitudeof the particle is

The amplitude of a particle in Simple Harmonic Motion (SHM) is given by the maximum displacement of the particle from its equilibrium position.

In the given equation, x = 4(Cos πt + Sin πt), the amplitude can be found by finding the maximum value of the function.

The maximum value of (Cos πt + Sin πt) can be found by using the trigonometric identity for the sum of two sine waves, which is √(a² + b² + 2ab cos φ), where a and b are the amplitudes of the sine waves and φ is the phase difference between them.

In this case, a = b = 1 (the coefficients of Cos πt and Sin πt), and φ = π/2 (the phase difference between Cos πt and Sin πt).

So, the maximum value of (Cos πt + Sin πt) = √(1² + 1² + 211 cos π/2) = √2.

Therefore, the amplitude of the particle is 4 * √2 = 5.66 units.