A body of mass 1 kg is executing simple harmonic motion. Its displacement 𝑦 cm at 𝑡 seconds is given by, 𝑦=6sin100𝑡+𝜋4. Its maximum kinetic energy is

The maximum kinetic energy (K.E.) in a simple harmonic motion is given by the formula:

K.E. = 1/2 * m * ω² * A²

where: m = mass of the body = 1 kg ω = angular frequency A = amplitude of the motion

From the given equation, y = 6sin(100t + π/4), we can identify the amplitude and the angular frequency.

The amplitude A is the coefficient of the sine function, which is 6 cm = 0.06 m (since 1 cm = 0.01 m).

The angular frequency ω is the coefficient of t in the argument of the sine function, which is 100 rad/s.

Substituting these values into the formula for K.E., we get:

K.E. = 1/2 * 1 kg * (100 rad/s)² * (0.06 m)² = 0.5 * 10000 * 0.0036 = 18 Joules

So, the maximum kinetic energy of the body is 18 Joules.