a) Acceleration is zero
b) Speed is zero
a) The equation of the simple harmonic motion is
x = A cos (wt +φ)
where
A = amplitude of the movement,
w= angular velocity and
φ = phase
Body acceleration is
a = d²x / dt²
dx / dt = - A w sin (wt + φ)
a = d²x / dt² = - A w² cos (wt + φ)
when it is not stretched x = 0
The spring is released at maximum elongation, φ = 0
0 = A cos wt
Cos wt = 0
wt = π / 2
a = -A w² cos π/2 = 0
Acceleration is zero
c) When the spring is compressed x = A
Speed (v) = dx / dt
v = - A w sin wt
A = A cos wt
cos wt = 1
wt = 0, π
v = -A w sin 0 = 0
Speed is zero
Complete question:
A mass is connected to a spring and is allowed to move horizontally. The mass is at a position L when the spring is unstretched. The mass is then moved, stretching the spring, and released from rest. It then moves with simple harmonic motion. (a) At the instant that the mass passes through the position where the spring is unstretched, what can be said about its instantaneous acceleration? Grade Summary It is maximum. OIt is zero It is non-zero but not maximum Potential per attempt) Hint I give up 1% -ム33%Part (b) At the instant that the spring is compressed the most, what can be said about the magnitude of its instantaneous velocity?
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