Question

In: Physics

3. A 1.50kg mass on a spring has a displacement as a function of time given...

3. A 1.50kg mass on a spring has a displacement as a function of time given by the

    equation:

x(t) = (7.40cm)cos[(4.16s-1)t – 2.42].

     Find,

  1. =
  1. the force constant of the spring;

  1. the maximum speed of the mass;
  1. the maximum force on the mass;
  1. at t= 1.00s, find the mass’s
    1. the position,
    2. the speed,
  1. the acceleration
  1. the force on the mass

Solutions

Expert Solution

Given,

Mass is

Displacement is

Speed can be obtained by differentiating this function with respect to time. Therefore,

Acceleration can be obtained by differentiating this speed function with respect to time. Therefore,

Let be the force constant of the spring.

Then we have, force

Speed is maximum when the sin value in the speed function is maximum (that is 1). Therefore, maximum speed is,

Force is maximum when acceleration is maximum. Therefore, make the value of cos in the acceleration function as 1. Therefore, we have

Therefore, maximum force is

The negative sign in these values just shows that they will be in the opposite direction as that of displacement. Consider their magnitudes only as maximum values.

Now, at time ,

Position is,

Speed is,

Acceleration is,

Force on the mass is,


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