Question

A spring hanging from the ceiling vibrates up and down. it's vertical position at time (t) is given by f(t)=4 sin(3t).

(a) Find the velocity of the spring at time t.

(b) What is the spring's maximum speed.

(c) what is location when it reaches its maximum speed.

Answer 1

for a .. i took the first derivative which is 4 cos(3t).3 = 12 cos(3t)

Answer 2

and for (b) .. s it 12 ?
=_=

Answer 3

;))

Answer 4

Help Me or im gonna Die thinking o(>< )o

Answer 5

(━┳━ _ ━┳━)

Answer 6

Me is too Dump to Solve this (⇀‸↼‶)7

Answer 7

vertical position is given which is distance.so f'(t)=4cos(3t)

Answer 8

it is velocity

Answer 9

o_o aha .. what about (b) ? =..= its killing me

Answer 10

Vmax = A*ω and ω = √(k/m).Maximum speed is found by this formula.

Answer 11

r u sure ? :l

Answer 12

k i will try
but what us a and w ?

Answer 13

u r right.but we must have to solve it by some derivative method.i have just finished the preparation for my exam which is going to b held tomorrow.so now i m mentally tired.could not get any solution right at this time.sorry.i will tell u later if u could not solve it.but if u solve it then msg me plz.thanks n good night

Answer 14

:l

Answer 15

Yes its 12 for (b)

Answer 16

(c) it comes to its mean position when it reaches its maximum speed

Answer 17

(c) you get max speed when t=0
Substitute t=0 in f(t) and f(t) will become zero which shows that velocity is max at mean position

Answer 18

You could also find a(t) and find where that = 0 to find the max I think

Answer 19

okie .. :l

Answer 20

thanx ppl =_='

Answer 21

i think im gonna close this question :B .. can't solve it anyway

Answer 22

u still not satisfied by answers?

Answer 23

first derivative is 12cos(3t).which is velocity.
and the maximum speed is 12 coz maximum value of cos is 1and if u put 1 in equation f't=12cos(3t) in place of cos(3t) u get maximum speed which is 12.now when u have maximum speed 12 and u know t=0 because cos(3t)=1 only when 3t=0 as cos0=1.so now put t=0 in first equation f(t)=4sin(3t) and you get location which is zero.that's ans of c.