Two shms are represented by the equations, y_1 = 15 sin 6t and y_2 = 18 sin (6t + pi/4). If the vibrating particles have the same mass find (i) ratio of maximum velocities (ii) ratio of time periods and (iii) ratio of total energies.

Two shms are represented by the equations, y_1 = 15 sin 6t and y_2 = 1

1.	Two shms are represented by the equations, y_1 = 15 sin 6t and y_2 = 18 sin (6t + pi/4). If the vibrating particles have the same mass find (i) ratio of maximum velocities (ii) ratio of time periods and (iii) ratio of total energies.
Answer» Solution :Amplitude of the first shm `= a_1, = 15` cm Amplitude of the second shm `= a_2, = 18 cm` Angular VELOCITY `= OMEGA= 6` rad/s Time period `=(2pi)/omega=(2pi)/6=pi/3s` Let the mass of each particle m Ratio of maximum value of velocities of the PARTICLES `=(a_1omega)/(a_2omega)=a_1/a_2=15/18=6/6` Ratio of PERIODS `=(pi//3)/(pi//3)=1` Ratio of total energies `=(1//2momega^2a_1^2)/(1//2momega^2a_2^2)=15^2/18^2=25/36`