Question

spring block system is undergoing horizontal oscillation at what distance from mean position the kinetic energy and the potential energy of a system become equal

Answer 1

• Assuming initial phase=0,
• x= a*cos(wt)
• v=- w*a sin(wt)
• K.E =0.5 mv^2 = 0.5 w^2 a^2 sin^2(wt)
• K.E max = 0.5 w^2 a^2
• Half this value is 0.5 w^2 a^2 *0.5
• So, sin^2(wt) should be equal to 0.5 to get what you are asking.
• Or solving,
• t =(1/w)* arcsin (sqrt(0.5))
• t = (1/w)*(5*pi/4)
• This is your required formula

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