Calculus Calculus Math Forum

 March 15th, 2011, 10:57 AM #1 Newbie   Joined: Mar 2011 Posts: 1 Thanks: 0 Please help me with my calculus homework question :( can someone please explain this to me?? I can just copy of the answer from my classmates but I really want to understand this I tried asking my professor and a teacher in the math help center but I still don't get it I don't know their is something with this question XD or maybe me? But please, I don't want you to give me the answer! I just want help with the explanation Thank you The position at any time t of a spring moving is given by f(t)=4cos(2t) Find the positions of the spring when it has (i) zero velocity (ii)maximum velocity (iii) minimum velocity
 March 15th, 2011, 11:34 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Please help me with my calculus homework question :( The velocity is the first derivative, so calculate that and find when it equals zero. Velocity is maximized (minimized) when its derivative (i.e. the acceleration) equals zero.
 March 15th, 2011, 11:35 AM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: Please help me with my calculus homework question :( We are given the position as: $f(t)=4\cos(2t)$ Velocity is defined as the time rate of change of position, or the rate of change of position with respect to time. Thus: $v(t)=\frac{df}{dt}=-8\sin$$2t)$ To find when v(t) = 0, we set: $\sin(2t)=0$ This will occur when $2t=n\pi$ where n is a non-negative integer (assuming 0 ? t) Thus $f(n\pi)=\text{ ?}$ gives the position of the spring when v(t) = 0. To find when v(t) is at its maximum, we merely observe that the sine function is at a maximum when its angle is $\frac{\pi}{2}+2n\pi=\frac{\(4n+1$$\pi}{2}$, so we find the position of maximum velocity to be: $f$$\frac{\(4n+1$$\pi}{2}\)=\text{ ?}$ If you think of a mass on a spring undergoing simple harmonic motion, its velocity is zero when it is furthest from equilibrium, and its velocity is at its greatest at equilibrium, since every time it passes the equilibrium point, it is experiencing a retarding force. Hooke's law, which governs simple harmonic motion states that the force on the object is proportional to its displacement from equilibrium and in the opposite direction of the displacement.

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