A particle of mass m is executing oscillations about the origin on the $$x-axis$$. Its potential energy is $$U(x)=k$$|x|$$3$$, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

Question

A particle of mass m is executing oscillations about the origin on the $$x-axis$$. Its potential energy is $$U(x)=k$$|x|$$3$$, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

Infinity Learn · Accepted Answer

$$U=k$$|x|$$3$$⇒$$F=$$−$$dUdx=$$−$$3k$$|x|$$2$$    ........(i) Also, for SHM, $$x=asin$$⁡ωt and $$d2xdt2+$$ω$$2x=0$$⇒ Acceleration $$a=d2xdt2=$$−ω$$2x$$⇒$$F=ma=md2xdt2=$$−mω$$2x$$     .......(ii) From eqs. (i) and (ii), we get ω$$=3kxm$$⇒$$T=2$$πω$$=2$$$$π$$$$m3kx=2$$$$π$$$$m3k(asin$$⁡ω$$t)$$⇒T∝$$1a$$

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is $U (x) = k | x |^{3}$ , where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

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A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x)=k|x|3, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

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A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is $U (x) = k | x |^{3}$ , where k is a positive constant. If the amplitude of oscillation is a, then its time period T is