Question

A body is moving in simple harmonic motion. Its position is modeled by s=sin(t)+cos(t), where s is measured in meters and t in seconds

a. Find the body’s velocity, speed, acceleration, and jerk at time t=pi/4 seconds
b. Find the time when the velocity is zero on [0,5]
c. Describe the motion of the body from t = 0 to t = 5 seconds

Answer 1

did you find the first and 2nd derivatives?

Answer 2

and 3rd derivative of s for "jerk"

Answer 3

PART A
velocity(time)= s'(t)=v(t)=cos(t)-sin(t)
a(t)=v'(t)=s''(t)=-sin(t)-cos(t)
j(t)=a'(t)=s'''(t)=-cos(t)+sin(t)

v(pi/4)=cos(pi/4)-sin(pi/4)=[sqrt(2)/2]-[sqrt(2)/2]=0
a(pi/4)=-sin(pi/4)-cos(pi/4)=-[sqrt(2)/2]-[sqrt(2)/2]=-sqrt(2)
j(pi/4)=-cos(pi/4)+sin(pi/4)=-[sqrt(2)/2]+[sqrt(2)/2]=0

Answer 4

ok i have to go now but ill be on so look later! thanks:)

Answer 5

*to

Answer 6

PART B
v(t)=0=cos(t)-sin(t)
cos(t)=sin(t)
tan(t)=1
t={pi/4; pi+pi/4}