A 2kg block is resting on a frictionless surface and attached to ahorizontal spr

Question

A 2kg block is resting on a frictionless surface and attached to ahorizontal spring that ha a spring constant of 32 N/m. I pull themass back 25 cm and release the mass- it moves in simple harmonicmotion. Unfortunately, I'm a little slow and start my timer 0.5seconds after I release the mass. a) Where is the mass when I start my timer b) Write an equation that represents the position of the massas a function of time( using the timer as your timereference) c) When my timer reads 3.0 seconds, where is the mass? d) When my timer reads 3.0 seconds, how fast is the masstraveling, and in what direction is it traveling. e) at what time(s) is the mass at maximum velocity? a) Where is the mass when I start my timer b) Write an equation that represents the position of the massas a function of time( using the timer as your timereference) c) When my timer reads 3.0 seconds, where is the mass? d) When my timer reads 3.0 seconds, how fast is the masstraveling, and in what direction is it traveling. e) at what time(s) is the mass at maximum velocity?

Explanation / Answer

Since we know that x(t)= Acos(t) where A= 0.25m and =2f=(k/m) = 157 rad/s then T= (1/2)(m/k) T= (1/2)(2.0/32) T= 0.040s a) Where is the mass when I start my timer since you have started the timer 0.5 seconds later the blockhas moved n= 0.5/ 0.04= 12.5 cycles or in a middle of acycle b) Write an equation that represents the position of the massas a function of time( using the timer as your timereference) We have to introduce a phase shift of -12.5 x 2 tocompensate for your time delay x(t)= -Acos(t - 12.5 x 2 )  or x(t)= -Acos(t - ) since =157rad/s x(t)= -Acos(157t - ) c) When my timer reads 3.0 seconds, where is the mass? Just plug 3.0 s into x(t)= -Acos(157t - ) d) When my timer reads 3.0 seconds, how fast is the masstraveling, and in what direction is it traveling. v(t)= dx/dt = 157Asin(157t - ) (Hintset your calculator to radians) e) at what time(s) is the mass at maximum velocity? Vmax = 157A at 157t - = /2 oractually at 157t - = 2n /2 wheren=1,2,3...(periodic motion it is ...) This is it Have fun. a) Where is the mass when I start my timer since you have started the timer 0.5 seconds later the blockhas moved n= 0.5/ 0.04= 12.5 cycles or in a middle of acycle since you have started the timer 0.5 seconds later the blockhas moved n= 0.5/ 0.04= 12.5 cycles or in a middle of acycle b) Write an equation that represents the position of the massas a function of time( using the timer as your timereference) We have to introduce a phase shift of -12.5 x 2 tocompensate for your time delay x(t)= -Acos(t - 12.5 x 2 )  or x(t)= -Acos(t - ) since =157rad/s x(t)= -Acos(157t - ) c) When my timer reads 3.0 seconds, where is the mass? Just plug 3.0 s into x(t)= -Acos(157t - ) d) When my timer reads 3.0 seconds, how fast is the masstraveling, and in what direction is it traveling. v(t)= dx/dt = 157Asin(157t - ) (Hintset your calculator to radians) e) at what time(s) is the mass at maximum velocity? Vmax = 157A at 157t - = /2 oractually at 157t - = 2n /2 wheren=1,2,3...(periodic motion it is ...) This is it Have fun.

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