ω is the angular frequency. Your first expression is correct for a simple pendulum. The second is for a mass on a spring. Both are examples of SHM.ctwokay said:i derivative the equation i got θ=θmax*ω*sin(ωt)
the ω outside i know is angular velocity √(g/L) but inside ω is √(k/m)
where do i find k constant in this question?
Sure.ctwokay said:using PE and KE?
Sure you can. (I missed that you found an expression for angular speed.)i can't use that expression? as the prof said need to use that to find
That's really an expression for [itex]\dot{\theta}[/itex], not θ. Once you have the max value of [itex]\dot{\theta}[/itex], use it to find the max speed.ctwokay said:i derivative the equation i got θ=θmax*ω*sin(ωt)
That's not true. Both ω's are the same: The angular frequency (not angular speed) of a pendulum. ω is given by the formula you posted for a pendulum.ctwokay said:ya its θ˙ first derivative i can't find the symbol but the problem is how do i find ω inside of sin? as ω outside of sin is angular velocity which is dθ/dt
If you measure time from when it was let go, then you don't need a phase angle.ctwokay said:is there a phase angle?
No, not quite right. You have sin(ω) instead of sin(ωt). You could include t, but you want the maximum speed. What's the maximum value of sinωt?i put 8.6* √(9.81/2.42)*sin(√(9.81/2.42)) is that right or i have to include t also?
You want the maximum angular speed. Since the angular speed is proportional to sinωt, the maximum speed will be when sinωt is maximum. What's the maximum value of sinωt?ctwokay said:ok i converted the θ to rad,
the equation i put 8.6*2*pi*√(9.81/2.42)*sin(√(9.81/2.42)t) so sinωt is the max which is at the period of oscillation?
i have the period but it is release at t=0 i can't use t=0 as it is a reference when it is release, so t i have to use some other equation?
Doc Al said:You want the maximum angular speed. Since the angular speed is proportional to sinωt, the maximum speed will be when sinωt is maximum. What's the maximum value of sinωt?
No, nothing to do with that.ctwokay said:Erm is it ω=2∏/T=2∏f?
Good! +1 is the maximum value of the sine function.ctwokay said:either 1 or -1?
Good. In this case we're already using ω to stand for angular frequency. So rewrite this one as: v = (dθ/dt)r.ctwokay said:linear speed is v=ωr
A pendulum is a weight suspended from a fixed point that is able to swing back and forth due to the force of gravity.
A pendulum works by converting potential energy into kinetic energy as it swings back and forth. The force of gravity pulls the pendulum down as it swings, causing it to increase in speed until it reaches its maximum speed at the lowest point of the swing.
The maximum speed of a pendulum is affected by its length, the force of gravity, and the angle at which it is released. Longer pendulums and stronger gravitational forces will result in a higher maximum speed, while a larger release angle will result in a lower maximum speed.
The maximum speed of a pendulum can be calculated using the formula v = √(2gL(1-cosθ)), where v is the maximum speed, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the release angle.
Yes, there is a limit to the maximum speed of a pendulum. The maximum speed is determined by the length of the pendulum, the force of gravity, and the release angle. Once these factors reach their maximum values, the pendulum will not be able to swing any faster.