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 $$x=asin$$ω t and  $$d2xdt2+$$ω$$2x=0$$⇒acceleration  $$=d2xdt2=$$−ω$$2x$$⇒$$F=ma=md2xdt2=$$−mω$$2x$$                                  ...(ii) From equation (i) & (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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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