My answers for part c,d, and e are wrong. Please advise how to get correct answe

Question

My answers for part c,d, and e are wrong. Please advise how to get correct answer by showing steps. Thank you .

An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is

s = 5 cos t + 3 sin t, t ? 0,

where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.)

(a) Find the velocity and acceleration at time t.

(b) Graph the velocity and acceleration functions.

(c) When does the mass pass through the equilibrium position for the first time? (Round your answer to two decimal places.)
t = 30.97 s IS WRONG

(d) How far from its equilibrium position does the mass travel? (Round your answer to two decimal places.)
s = 3.17 cm IS WRONG

(e) When is the speed greatest? (Use n, a positive integer.)

0.54 + n?

0.54 + 2n?

    

2.11 + n?

2.11 + 2n?

2.65 + 3n?

v(t) = -5sint+cost a(t) = -5cost-sint My answers for part c,d, and e are wrong. Please advise how to get correct answer by showing steps. Thank you . An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is s = 5 cos t + 3 sin t, t ? 0, where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.) (a) Find the velocity and acceleration at time t. v(t) = -5sint+cost a(t) = -5cost-sint (b) Graph the velocity and acceleration functions. (c) When does the mass pass through the equilibrium position for the first time? (Round your answer to two decimal places.) t = 30.97 s IS WRONG (d) How far from its equilibrium position does the mass travel? (Round your answer to two decimal places.) s = 3.17 cm IS WRONG (e) When is the speed greatest? (Use n, a positive integer.) 0.54 + n? 0.54 + 2n? 2.11 + n?

Explanation / Answer

c) For equilibrium s=0

5 cos t + 3 sin t =0

Sqrt(34) [sin(t + 1.03)] = 0

t + 1.03= 0, pi, 2pi.....

t = 2.11

d) For this case velocity =0

-5sint + 3cost =0

Sqrt(34) [ sin( t - 0.54)] = 0
t - 0.54 = 0, Pi, 2Pi,...
t = 0.54

Put this value in s

s = 5cost+3sint

    = 5 cos (0.54) + 3 sin ( 0.54)

      =4.29 + 1.54

      = 5.83 cm

e) speed greatest when acceleration zero

-5cost - 3sint =0

-[5cos(t) + 3sin(t)] = 0
-Sqrt(34) [sin(t + 1.03)] = 0
(t + 1.03) = 0, Pi, 2Pi, ...

t = 2.11 +n

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