The displacement of a particle is represented by the equation $$y=5$$ $$cos3$$$$π$$$$2$$−$$2$$π t where y is displacement ω is angular frequency in metre and t is given in instant of time in h the motion of the particle is

Question

The displacement of a particle is represented by the equation  $$y=5$$  $$cos3$$$$π$$$$2$$−$$2$$π  t  where y is displacement  ω is angular frequency in metre and t is given in instant of  time in h the motion of the particle is

Infinity Learn · Accepted Answer

The equation  $$y=5$$  $$cos3$$$$π$$$$2$$−$$2$$π  t represents simple harmonic motion which takes  the form $$y=5$$  $$sin2$$π  $$t+$$π$$2$$ The equation $$y=5$$  $$cos3$$$$π$$$$2$$−$$2$$π  t  can be  Written $$asy=5cos$$⁡$$2$$$$π$$t−$$3$$$$π$$$$2($$∵$$cos$$⁡$$($$−θ$$)=$$$$cos$$⁡θ$$)$$⇒$$y=5cos$$⁡π$$2+2$$$$π$$t−$$2$$π∵$$3$$$$π$$$$2=2$$π−π$$2$$⇒$$y=5cos$$⁡π$$2+2$$$$π$$$$t($$∵$$cos$$⁡$$(2$$π−θ$$)=$$$$cos$$⁡θ$$)y=$$−$$5sin$$⁡$$2$$$$π$$t∵$$cos$$⁡π$$2+$$θ$$=$$−$$sin$$⁡θHence time period is $$1$$ hour

The displacement of a particle is represented by the equation $y = 5 \cos (\frac{3 π}{2} - 2 π t)$ where y is displacement $ω$ is angular frequency in metre and t is given in instant of time in h the motion of the particle is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The displacement of a particle is represented by the equation y=5 cos3π2−2π t where y is displacement ω is angular frequency in metre and t is given in instant of time in h the motion of the particle is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The displacement of a particle is represented by the equation $y = 5 \cos (\frac{3 π}{2} - 2 π t)$ where y is displacement $ω$ is angular frequency in metre and t is given in instant of time in h the motion of the particle is