The displacement of a particle executing simple harmonic motion is given by
x = a sin $ω$ t + a cos $ω$ t
The total energy of the particle is

Question

The displacement of a particle executing simple harmonic motion is given by x $$=$$ a $$sin$$ ωt $$+$$ a $$cos$$ ωt The total energy of the particle is

Infinity Learn · Accepted Answer

Given x $$=$$ a $$sin$$ ωt $$+$$ a $$cos$$ ωt                …….. (1)The$$ displacement equation of a simple harmonic motion is x $$=$$ A $$sin$$ $$($$ωt $$+$$ ϕ$$)where$$ A $$=$$ amplitude and ϕ $$=$$ phase constant. x $$=$$ A $$sin$$ ωt $$cos$$ϕ $$+$$ A $$cos$$ ωt $$sin$$ ϕ         …….. $$(2)Comparing$$ $$(1) with (2) we get A $$cos$$ ϕ $$=$$ a    (3)and$$ A $$sin$$ ϕ $$=$$ a    $$(4)Squaring$$ and adding Eqs. $$(3) and (4) we get $$A2$$ $$=$$ $$a2$$ $$+$$ $$a2$$  ⇒   $$A2$$ $$=$$ $$2a2$$∴ Energy $$=$$   $$12$$ m   ω$$2$$ $$A2$$ $$=$$ m   ω$$2$$ $$a2So$$ the correct choice is (b).

The displacement of a particle executing simple harmonic motion is given by
x = a sin $ω$ t + a cos $ω$ t
The total energy of the particle is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The displacement of a particle executing simple harmonic motion is given by x = a sin ωt + a cos ωt The total energy of the particle is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The displacement of a particle executing simple harmonic motion is given by
x = a sin $ω$ t + a cos $ω$ t
The total energy of the particle is