Aparticle oscillates harmonically x = a cos(ωt + φ0), with amplitude 9 m, angular frequency π s −1, and initial phase π 3 radians. every now and then, the particle’s kinetic energy and potential energy happen to be equal to each other (k = u). when does this equality happen for the first time after t = 0?

Explanation:

As we know that the equation of particle position is given as

Now the speed of the particle is given as

now we know that potential energy and kinetic energy is equal

so we have

so we will have

the force on the thing and the distance the force moves the thing

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.