A ping-pong ball is caught in a vertical plexi-glass column in which the air flow alternates sinusoidally with a period of 60 seconds. The air flow starts with a maximum upward flow at the rate of -0.4 m/s and at t = 30 seconds the flow has a minimum (upward) flow of rate of -0.4 m/s. (To make this clear: a flow of -5m/s upward is the same as a flow downward of 5 m/s.
The ping-pong ball is subjected to the forces of gravity (-mg) where g= 9.8m/s^2 and forces due to air resistance which are equal to k times the apparent velocity of the ball through the air.
a: What is the average velocity of the air flow?
b: Write a formula for the velocity of the air flow as a function of time.
c: Write the differential equation satisfied by the velocity of the ping-pong ball (relative to the fixed frame of the plexiglass tube.) The formulas should not have units entered, but use units to trouble shoot your answers. Your answer can include the parameters m, k, t, and v
d: Find the amplitude and phase shift of this solution. You do not need to enter units.
e: Find the general solution by adding on a solution to the homogeneous equation. Calculate the specific solution that has initial conditions t=0 and w(0) = 4
The ping-pong ball is subjected to the forces of gravity (-mg) where g= 9.8m/s^2 and forces due to air resistance which are equal to k times the apparent velocity of the ball through the air.
a: What is the average velocity of the air flow?
b: Write a formula for the velocity of the air flow as a function of time.
c: Write the differential equation satisfied by the velocity of the ping-pong ball (relative to the fixed frame of the plexiglass tube.) The formulas should not have units entered, but use units to trouble shoot your answers. Your answer can include the parameters m, k, t, and v
d: Find the amplitude and phase shift of this solution. You do not need to enter units.
e: Find the general solution by adding on a solution to the homogeneous equation. Calculate the specific solution that has initial conditions t=0 and w(0) = 4