In: Physics
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,
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,