A 200 gram block is attached to a spring with a spring constant of 8 N/m. The spring oscillates horizontally on a frictionless surface. Its velocity is 80 cm/s when x = - 4.2 cm.

Question

a. What is the amplitude of oscillation?

b. What is the block’s maximum acceleration?

c. What is the block’s position when the acceleration is maximum?

d. What is the speed of the block when x = 2.5 cm?

I think I already got a and b but am confused on the other two parts

Answer 1

Acceleration is a maximum where the displacement from equilibrium (and thus the spring force) is a maximum.

Since KE + PE is a constant,

(1/2) k X^2 + (1/2) m V^2 = C
= 4*(0.042)^2 + (0.100)(0.080)^2

Note that I am using meters and not centimeters for x and V.

Once you know that constant, the total energy, you can compute BV at any value of x.

Answer 2

Okay I think I calculated that correctly but all the equations I see to use incorporate time which I do not have...I am sorry I am just really confused and my brain is about fried.

Answer 3

Nevermind, I'm dumb thanks!

Answer 4

The method that I used above is based upon conservation of energy and does not require you to know or calculate the time that x or V has a particular value. It is a useful shortcut.

"BV" in my previous post should be just V. Sloppy typing.