Question

When a mass attached to a spring oscillates without friction, its position relative to the equilibrium position
(s = 0)
is a function of time t given by,
s(t) = A sin(Bt + C)
for some constants A, B, C, where A > 0 and B > 0. Write a formula for the velocity and acceleration of the object in terms of time t.
I got
Velocity: ABcos(Bt+C)
Acceleration: -AB^2(sin(Bt+C)
But I’m having trouble with this part
What is the acceleration of the object when it is at its furthest distance from the equilibrium position?

Answer 1

velocity = v(t) = s'(t) = ABcos(Bt+C)
Acceleration = v'(t) = -AB^2sin(Bt+c)

so what you done is good.

now what is the furthest distance ? you see the amplitude of s(t) is A
and it happens when sin(Bt+C) is +\-1
so you can see when sin(Bt+C) is +\-1 the magnitude of the acceleration is AB^2.

and it's a known fact that when that every time the maximum of the distance achieved the body has it's maximum acceleration.

Answer 2

Interesting!
I thought that we would find the maximum distance at one of the points where velocity equaled zero.

Answer 3

or where the acceleration equaled zero

Answer 4

yes.. maximum distance -> zero velocity and maximum acceleration

Answer 5

Awesome, thank you!

Answer 6

as well zero distance -> maximum velocity and zero acceleration

Answer 7

yw.. good luck!:)

Answer 8

Okay so for the actual answer it would be two numbers, pi/4 and -3pi/4 ?

Answer 9

I solve for when sin(x)= +-1

Answer 10

The acceleration will just be -AB^2 or AB^2

Answer 11

is there a different question asking about it's position or time at these locations?

Answer 12

No, it's a fairly simple problem. I just have holes in my education in respect to trig functions!
but I would have never considered AB^2 to be the answer

Answer 13

So I would just imagine the graph and see where the amplitude is and that would be my answer because the velocity would be zero at the max and min points

Answer 14

I think I understand this, thank you

Answer 15

as i wrote the maximum acceleration is the amplitude which is AB^2.