A particle is executing simple harmonic motion. The equation of motion is given by $$d2xdt2+4x=0$$. Then their time period of oscillation is (in$$ $$seconds)

Question

A particle is executing simple harmonic motion. The equation of motion is given by $$d2xdt2+4x=0$$. Then their time period of oscillation is (in$$ $$seconds)

Infinity Learn · Accepted Answer

A simple harmonic motion can be represented by the equation  $$a=$$−ω$$2x$$ . where  acceleration a can be written as $$d2xdt2$$ . Hence $$d2xdt2=$$−ω$$2x$$ . Writing the given equation $$d2xdt2+4x=0$$ in the above form, we get  $$d2xdt2=$$−$$4x$$. Comparing this with the above equation, we get  ω$$2=4$$. Taking square root on both sides  ω$$=2Using$$ the relation  ω$$=2$$$$π$$T, we get  $$2=2$$$$π$$THence, time period of oscillation is π s

A particle is executing simple harmonic motion. The equation of motion is given by $\frac{d^{2} x}{d t^{2}} + 4 x = 0$ . Then their time period of oscillation is (in seconds)

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A particle is executing simple harmonic motion. The equation of motion is given by d2xdt2+4x=0. Then their time period of oscillation is (in seconds)

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A particle is executing simple harmonic motion. The equation of motion is given by $\frac{d^{2} x}{d t^{2}} + 4 x = 0$ . Then their time period of oscillation is (in seconds)