Please help me with this calculus problem!

The position, x, of the midpoint of the vibrating violin string is described by the formula x=0.05cos(880pi(t)), where x is measured in centimeters and t is measured in seconds.

i) Determine the formulas for the velocity and the acceleration of the midpoint of the string.

ii) Determine the maximum speed of the vibration of the string in cm/s

iii) Show that the acceleration and position satisfy the differential equation, d^x/dt^2 + (880pi)^2x=0

Question

Please help me with this calculus problem!



The position, x, of the midpoint of the vibrating violin string is described by the formula x=0.05cos(880pi(t)), where x is measured in centimeters and t is measured in seconds.

i) Determine the formulas for the velocity and the acceleration of the midpoint of the string.

ii) Determine the maximum speed of the vibration of the string in cm/s

iii) Show that the acceleration and position satisfy the differential equation, d^x/dt^2 + (880pi)^2x=0