Physics Help Forum Particle executing simple harmonic motion

 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

Apr 10th 2015, 06:23 PM   #1
Junior Member

Join Date: Mar 2015
Posts: 9
Particle executing simple harmonic motion

This refers to question 14. in the scan I attached. A particle executes simple harmonic motion with amplitude of 3.0 cm. At what displacement from the midpoint of its motion does its speed equal one half of its maximum speed? The answer to the problem is 2.6 cm. I don't know how to obtain this answer. I have included my work. Thanks.
Attached Files
 Scan0003.pdf (859.1 KB, 7 views)

 Apr 11th 2015, 01:30 AM #2 Senior Member     Join Date: Apr 2008 Location: Bedford, England Posts: 668 You are on the right track, but getting bogged down in the equations Taking the displacement motion as a cosine function, then (as you correctly indicate) the speed will be given by a sine function. Ignore scaling factors (for now) you want to know when the sine function is at half its maximum. The maximum for an unscaled sine function is 1.0 so we want to know when the sine function is 0.5. The inverse sine of 0.5 is 30 (degrees), what is the displacement (cosine function) at 30 (degrees)? (don't forget to bring back the scaling factor at this point) Note that I have been a little bit lazy, I haven't used omega t or phi or even radians, but the answer is the same, the rest of the equation is (in this example) superfluous (for other problems they may be crucial). I guess it is a bit of a knack identifying the important features of the equations for a given problem. I can definitely remember floundering in almost exactly the same manner as you during my school days. __________________ You have GOT to Laugh ! Last edited by MBW; Apr 11th 2015 at 01:33 AM.

 Tags executing, harmonic, motion, particle, simple

,

,

,

### worked examples involving particle executing simple harmonic motion

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post unstopabl3 Waves and Sound 4 Sep 22nd 2010 06:08 AM jddery Kinematics and Dynamics 0 Feb 7th 2010 10:59 AM Budhiman Advanced Electricity and Magnetism 3 Mar 27th 2009 11:24 AM Budhiman Advanced Mechanics 4 Mar 12th 2009 04:58 AM agber david Advanced Mechanics 1 Mar 11th 2009 01:11 AM