A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the motion is

Question

A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the motion is

Infinity Learn · Accepted Answer

Let the acceleration be f; $$f=$$−ω$$2xTherefore$$, distance of the particle from the centre at any time t is given by $$x=rcos$$⁡$$($$ω$$t)$$ where r is the amplitude when $$t=1s$$,$$x=r$$−a∴ (r$$−$$a)=rcos$$⁡ω$$cos$$⁡ω$$=r$$−ar     ........$$(i) When $$t=2s$$,$$x=r$$−a−b, therefore  r−a−$$b=$$$$cos$$⁡$$2$$ω∴ r−a−$$b=r2cos2$$⁡ω−$$1$$    ………..(ii)Substituting$$ the value of $$cos$$⁡ω from Eq. $$(i) in Eq. (ii), we get r−a−$$b=r2(r$$−$$a)2r2$$−$$1=2(r$$−$$a)2r$$−r∴ $$r(3a$$−$$b)=2a2$$⇒$$r=2a23a$$−b

A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest it travels a distance $a$ and in the next second it travels a distance $b$ in the same direction. The amplitude of the motion is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material