Physics problem help. (Please do..)?

Question

Problem 1:  

The displacement of a mass undergoing Simple Harmonic Motion is given as:  x = xo coswt.

Show that  v = +/- w  square root [ x0^2 - x^2].




Problem 2: 

A mass of 1.5 kg is undergoing SHM. 
Amplitude: 0.5m
Mass: 1.5kg

A: What is the maximum restoring force?

B: What is the magnitude of the restoring force when the mass is 0.25m from it's original position/

JullyWum · Accepted Answer

1) displacement x = xₒ cos(ωt) ------- (1)

velocity = dx/dt .. .. v = - xₒω sin(ωt) -------- (2)

sin²(ωt) + cos²(ωt) = 1, giving ..
sin²(ωt) = 1 - cos²(ωt)
 
substituting for cos(ωt) from (1) .. sin²(ωt) = 1 - (x/xₒ)²

substituting for sin(ωt) from (2) .. [v/(xₒω)]² = 1 - (x/xₒ)² 
√ both sides  .. .. .. .. .. .. .. .. .. .. v/(xₒω) = √{1 - (x/xₒ)²} 
v = (xₒω).√{1 - (x/xₒ)²} 
v = (xₒω).√{(xₒ²- x²) / xₒ²} = (xₒω).1/xₒ.√(xₒ²- x²) ..

►v = ω.√(xₒ²- x²) .. 
As there is a symmetrical velocity about the equilibrium position .. +/- denotes possible velocities (in opposite directions).

2A) F(max) = m*a(max)

Using the shm equation  a = (-)ω².x ---- (x= displacement from equilibrium)
a(max) = (-)ω².x(max) .. .. a(max) = ω².xₒ

F(max) = m*ω².xₒ .. we have a value for m (1.50kg) and xₒ (0.50m) .. but that's not enough information.

btw .. 'full' only needs 3* .. f***

Physics problem help. (Please do..)?

1 Antwort