Conceptual Questions Fluids and Simple Harmonic motion

[vivekfan]

Homework Statement

1. Do you use the equation of continuity and Bernoulli's equation simultaneously in a question? When do you use them?

2. In simple harmonic motion, why is the velocity shifted to left of the displacement by pi/4?

Homework Equations

pressure + .5density x velocity ^2 + density x g x y (initial)= the same thing (final)

A1V1=A2V2 (continuity)

x(t)=xmaxcos(wt + phi) here w=omega

The Attempt at a Solution

I've been reading my book, but I am confused about these issues. Please help.

 

[Doc Al]

1. Do you use the equation of continuity and Bernoulli's equation simultaneously in a question?

Sure.

When do you use them?

In all sorts of problems involving streamlined fluid flow. For example, flow through a pipe of varying height and cross-sectional area.

2. In simple harmonic motion, why is the velocity shifted to left of the displacement by pi/4?

I think you mean pi/2. To see this, imagine a ball on a spring oscillating back and forth along the x axis. When it passes through the equilibrium point (going towards +x, say) its speed is at its maximum positive value while the displacement is at zero. When it gets to maximum displacement, the speed now is zero. When it returns to equilibrium, its displacement is again zero, but the speed is maximum negative. And so on. Sketch out the diagrams of displacement and velocity (both sinusoids) and you'll see that the velocity graph looks exactly like the displacement graph, just slid over to the left by pi/2.