# Vmax and Amax known.

## Homework Statement

An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.11 m/s, and its maximum acceleration is 6.65 m/s2. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum

## The Attempt at a Solution

Not sure where to start

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You can use equation for a simple harmonic motion (distance as a cosine or sine function), and keep differentiating it to find the time of maximum speed and acceleration.

or use energy conservation

at which position do you think speed and acc. be max

Still not getting it..

or use energy conservation

at which position do you think speed and acc. be max
Vmax will occur when x=0

Amax will occur when V=0

gneill
Mentor
Vmax will occur when x=0

Amax will occur when V=0
V is not a position.

V is not a position.
well Amax will occur at xmax

Jow can you write the energies of body at x=0 and x=max?

gneill
Mentor
well Amax will occur at xmax
Yes, and what position is that, where position means angle(s).

Still not understanding can you lay it out a bit

gneill
Mentor
In simple harmonic motion the displacement follows a sine (or cosine, your choice) function. You should have seen this in class or in your text.