1. Answer the question in detail:Braking radiation Spectrum of braking radiation. Short wave boundary. Solve the problems. A) A body is in simple harmonic motion along the x axis. Its displacement varies with time according to the equation S=0.4cos(pi t+pi /4) where t is in seconds and the angles in the parentheses are in radians.a) Determine the amplitude, frequency ,and period of the motion. (b)Calculate the velocity of the body at time t=1s B) Radio waves travel through air at a speed of 3times 10^8ms^-1 Calculate the wavelength in air of radio waves of frequency 105 MHz. time dependence of the displacement of the body is given by the expression os((pi )/(3)t+(pi )/(2)) Find the expression for velocity of the body vartheta (t) se the answer:

) <br />a) The amplitude of the motion is the maximum displacement from the equilibrium position, which is given by the coefficient of the cosine function in the equation. In this case, the amplitude is 0.4 m.<br /><br />The frequency of the motion is given by the coefficient of t in the argument of the cosine function. In this case, the frequency is π rad/s.<br /><br />The period of the motion is the time it takes for the body to complete one full cycle of motion. It is given by the reciprocal of the frequency. In this case, the period is 2 s.<br /><br />b) The velocity of the body at any time t is given by the derivative of the displacement with respect to time. Taking the derivative of the given equation with respect to t, we get:<br /><br />v(t) = -0.4πsin(πt + π/4)<br /><br />Substituting t = 1 s into this equation, we get:<br /><br />v(1) = -0.4πsin(π + π/4) = -0.4πsin(5π/4) = -0.4π(-√2/2) = 0.4π√2/2 = 0.4√2π m/s<br /><br />B) The wavelength of a wave is given by the ratio of the speed of the wave to its frequency. In this case, the speed of the radio waves is 3 × 10^8 m/s and the frequency is 105 MHz or 105 × 10^6 Hz. Therefore, the wavelength is:<br /><br />λ = v/f = (3 × 10^8 m/s) / (105 × 10^6 Hz) = 2.86 m<br /><br />C) The velocity of the body is given by the derivative of the displacement with respect to time. Taking the derivative of the given equation with respect to t, we get:<br /><br />v(t) = -π/3sin(πt/3 + π/2)<br /><br />D) The velocity of the body is given by the derivative of the displacement with respect to time. Taking the derivative of the given equation with respect to t, we get:<br /><br />v(t) = -π/3sin(πt/3 + π/2)