A 200 g block connected to a light spring for which the force constant is 5 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5 cm from equilibrium and released from rest.
A 200 g block connected to a light spring for which the force constant is 5 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5 cm from equilibrium and released from rest.
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1. What if the block were released from the same initial position, x0 = 5 cm, but with an initial velocity of v0 = −0.1 m/s? Which parts of the solution change, and what are the new answers for those that do change?
2. Consider again the block–spring system in the last slide, whose position, velocity, and acceleration are given in part (d) of the problem. Find a general expression for all times at which the
block is located at x = 12A.
3. Suppose we measure the speed of the block at the instants found in the problem. At these instants, will the speed of the block be half the maximum speed?
Transcribed Image Text:A 200 g block connected to a light spring for which the force
constant is 5 N/m is free to oscillate on a frictionless, horizontal
surface. The block is displaced 5 cm from equilibrium and released
from rest.
x=0
wwwwwwww
m
t = 0
x₁ = A
V₁ = 0
(a) Find the period of its motion 1.2568 second
(b) Determine the maximum speed of the block 0.25 m/s
(c) What is the maximum acceleration of the block? 1.25 m/s^2
(d) Express the position, velocity, and acceleration as functions of
time in Sl units. x=5cos5t v=-25 cos5t a=-125cos5t
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