A particle of mass m is moving in a potential well, for which the potential energy is given by $$U(x)=U01$$−sinbx where $$U0$$ and a are constants. Then for small oscillations find time period

Question

A particle of mass m is moving in a potential well, for which the potential energy is  given by $$U(x)=U01$$−sinbx where  $$U0$$ and a are constants. Then for small  oscillations find time period

Infinity Learn · Accepted Answer

given $$PE$$ is $$U(x)=U01$$−sinbx then force is $$F=$$−dUdx differentiate given equation wrt x $$F=$$−$$bU0sinbx$$  For small oscillations, sinbx≈bx  ⇒$$F=$$−$$b2U0x---(1)$$ for simple harmonic motion $$F=-m$$ω$$2x---(2)$$ substitute $$eqn(2)$$ in (1) $$-m$$ω$$2x=$$−$$b2U0x$$ ω$$=b2U0m=2$$$$π$$T $$T=2$$$$π$$$$mb2U0=time$$ period of small oscillation here ω$$=angular$$ velocity; $$m=mass$$ ;$$x=displacement$$ of oscillator .

A particle of mass m is moving in a potential well, for which the potential energy is given by $U (x) = U_{0} (1 - \sin b x)$ where $U_{0}$ and a are constants. Then for small oscillations find time period

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A particle of mass m is moving in a potential well, for which the potential energy is given by U(x)=U01−sinbx where U0 and a are constants. Then for small oscillations find time period

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A particle of mass m is moving in a potential well, for which the potential energy is given by $U (x) = U_{0} (1 - \sin b x)$ where $U_{0}$ and a are constants. Then for small oscillations find time period