A mass oscillating on a spring has amplitude of 1.2m and a period of 2s.Deduce the equation for the displacement x if the timing starts at the instant when the masd has its maximum displacement. b)calculate the time interval from t=0 before the displacement is 0.08m


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Question Number 32757 by NECx last updated on 01/Apr/18

$A m a s s o s c i l l a t i n g o n a s p r i n g$ $h a s a m p l i t u d e o f 1.2 m a n d a p e r i o d$ $o f 2 s . D e d u c e t h e e q u a t i o n f o r$ $t h e d i s p l a c e m e n t x i f t h e t i m i n g$ $s t a r t s a t t h e i n s t a n t w h e n t h e m a s d$ $h a s i t s m a x i m u m d i s p l a c e m e n t .$ $b) c a l c u l a t e t h e t i m e i n t e r v a l f r o m$ $t = 0 b e f o r e t h e d i s p l a c e m e n t i s$ $0.08 m$
Commented by NECx last updated on 01/Apr/18

$T h i s w a s w h a t I d i d$ $x = A \cos ω t$ $\frac{d x}{d t} = - A ω \sin w t$ $a t t h e m a x i m u m d i s p l a c e m e n t$ $d x / d t = 0$ $∴ 0 = - A w s i n w t$ $s i n w t = 0$ $w t = 0, π, 2 π, . . . . . . . . . .$ $s i n c e w = 2 π / T$ $t h e n w = π$ $∵ t = {0, 1, 2, . . . . . . . .} s$ $∵ x = 1.2 c o s 0 w h e n t = 0$ $x = 1.2 c o s π w h e n t = 1$ $a n d s o o n . . . . .$ $T h i s d o e s n t s e e m t o m e l i k e t h e$ $r i g h t a n s w e r s o I^{'} m c o n f u s e d .$
Commented by NECx last updated on 02/Apr/18

$s o m e o n e p l e a s e h e l p . P l e a s e I^{'} v e$ $b e e n s t r u g g l i n g w i t h i t f o r a l o n g w h i l e$
Commented by NECx last updated on 02/Apr/18

$I t h i n k M r w 2 a n d A j f o u r$ $h a v e n o t b e e n o n l i n e .$ $R e a l l y o b v i o u s .$
Commented by float last updated on 03/Apr/18

$Amplitude A = 1.2 m$ $Period T = 2 s$ $∴ ω = \frac{2 π}{T} = \frac{2 π}{2 s} = π Hz$ $Therefore, x (t) = A \cos (ω t) = 1.2 \cdot \cos (π t) .$ $b) x (t) = 1.2 \cdot \cos (π t) = 0.08 m$ $∴ t = \frac{\arccos (\frac{0.08}{1.2})}{π} \approx 0.48 s$
Commented by NECx last updated on 03/Apr/18

$t h a n k s . . . w h a t i f {w e}^{'} r e a s k e d t o$ $f i n d t h e v e l o c i t y a t t h i s i n s t a n t ? ?$
	Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18

	$x = A c o s (\frac{2 Π}{T} t + θ) g i v e n A = 1.2 m T = 2 s e c$ $w h e n t = 0 x = A$ $A = A c o s (\frac{2 Π}{T} \times 0 + θ)$ $c o s θ = 1$ $θ = 0$ $x = A c o s (\frac{2 Π}{T} t)$ $c o s (\frac{2 Π}{T} t) = \frac{x}{A}$ $t = \frac{T}{2 Π} {c o s}^{- 1} (\frac{x}{A})$ $t = \frac{2}{2 \times 3.14} {c o s}^{- 1} (\frac{0.08}{1.2})$
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