A particle of mass m kept at the origin is subjected to a force F = ( pt − q x ) i ^ where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion

Question

A particle of mass m kept at the origin is subjected to a force F = ( pt − q x ) i ^ where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t = 0 with zero initial velocity. If p and q are positive constants, then : (1) The acceleration of the particle will continuously keep on increasing with time. (2) Particle will execute simple harmonic motion (3) The force on the particle will have no upper limit. (4) The acceleration of particle will vary sinusoidally with time. मूल बिन्दु पर रखे m द्रव्यमान के एक कण पर एक बल F = ( pt − qx ) i ^ लग रहा है जहाँ t व्यतित समय है तथा x

TestHub · Accepted Answer

​ F = pt − q x ⇒ ​ a = m 1 ​ ( pt − q x ) ⇒ ​ d t d a ​ = m [ p − q v ] ​ ⇒ ​ d t 2 d 2 a ​ = − m q ​ a [ = − ω 2 a ] ⇒ ω = m q ​ ​ ​

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