Answer to Question #245710 in Calculus for luka

Question #245710

A body oscillates with simple harmonic motion according to the equation x(t)=5sin(4pie.t+pie/4

(x in meters). At time t = 5 seconds what are : /(6 x


2.5mrks)


(a) the displacement (b) the velocity

(c) the acceleration (d) the phase of the motion

(e) the frequency (f) the period of the motion.


1
Expert's answer
2021-10-06T10:04:39-0400

(a)


x(5)=5sin(4π(5)+π4)=2.52 mx(5)=5\sin(4\pi(5)+\dfrac{\pi}{4})=2.5\sqrt{2}\ m


(b)


v(t)=20πcos(4πt+π4)v(t)=20\pi\cos(4\pi t+\dfrac{\pi}{4})

v(5)=20πcos(4π(5)+π4)=10π2 m/sv(5)=20\pi\cos(4\pi (5)+\dfrac{\pi}{4})=10\pi\sqrt{2}\ m/s

(c)


a(t)=80π2sin(4πt+π4)a(t)=-80\pi^2\sin(4\pi t+\dfrac{\pi}{4})

a(5)=80π2sin(4π(5)+π4)=40π22 m/s2a(5)=-80\pi^2\sin(4\pi (5)+\dfrac{\pi}{4})=-40\pi^2\sqrt{2}\ m/s^2

(d)


φ(t)=4πt+π4\varphi(t)=4\pi t+\dfrac{\pi}{4}

φ(5)=4π(5)+π4=81π4rad\varphi(5)=4\pi (5)+\dfrac{\pi}{4}=\dfrac{81\pi}{4} rad

(e)


f=4π2π=2 s1f=\dfrac{4\pi}{2\pi}=2\ s^{-1}

(f)


T=1f=12 sT=\dfrac{1}{f}=\dfrac{1}{2}\ s


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment