A body executes S.H.M. under the action of a force $$F1$$ with a time period $$7/6$$ seconds. If the force is changed to $$F2$$ it executes S.H.M. with time period $$7/8$$ seconds. If both the forces $$F1$$ and $$F2$$ act simultaneously in the same direction on the body, then its time period in seconds is

Question

A  body  executes S.H.M. under the action of a force $$F1$$ with a time period $$7/6$$  seconds.  If the force is changed to $$F2$$ it executes S.H.M. with time period $$7/8$$  seconds. If both the forces $$F1$$ and $$F2$$ act simultaneously in the same direction on  the body, then its time period in seconds is

Infinity Learn · Accepted Answer

For a body executing simple harmonic motion, the force can be written as $$F=m$$ω$$2y$$  For the first force $$F1=m2$$$$π$$$$T12y$$  and for the second force  $$F2=m2$$$$π$$$$T22y$$. On combining the two forces  $$F1+F2=Fnet$$ , where $$Fnet=m2$$$$π$$$$Tnet2y$$ Substituting this in the equation $$F1+F2=Fnet$$, we $$getm2$$$$π$$$$Tnet2y=m2$$$$π$$$$T12y+m2$$$$π$$$$T22y$$ From the question,  $$T1=76$$ s and  $$T2=78$$ $$s1Tnet2=672+8721Tnet2=10049Tnet2=49100$$ Therefore,  $$Tnet=710s$$

A body executes S.H.M. under the action of a force F₁ with a time period 7/6 seconds. If the force is changed to F₂ it executes S.H.M. with time period 7/8 seconds. If both the forces F₁ and F₂ act simultaneously in the same direction on the body, then its time period in seconds is

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A body executes S.H.M. under the action of a force F1 with a time period 7/6 seconds. If the force is changed to F2 it executes S.H.M. with time period 7/8 seconds. If both the forces F1 and F2 act simultaneously in the same direction on the body, then its time period in seconds is

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A body executes S.H.M. under the action of a force F₁ with a time period 7/6 seconds. If the force is changed to F₂ it executes S.H.M. with time period 7/8 seconds. If both the forces F₁ and F₂ act simultaneously in the same direction on the body, then its time period in seconds is