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Sagot :
The system will undergo simple harmonic motion, so at time,
t₁ = π/2( [tex]\sqrt{k/m}[/tex])
What is simple harmonic motion?
Simple harmonic motion is described as the periodic motion of a point along a straight line with an acceleration that is always toward a fixed point on that line and a distance from that point that is proportional to that acceleration.
The equation of motion for the simple harmonic oscillation of spring mass system is,
a(t) = -k/m x(t)
here, a(t) = is the acceleration at any time
k = is the spring constant, and
m = mass
The equation for displacement is given as,
x(t) = A cos ([tex]\sqrt{k/m}[/tex])t
here,
x(t) = is the displacement at any time.
A = is the amplitude of oscillations,
The velocity is given by,
v(t) = dx(t)/dt
The general expression of velocity for a simple harmonic motion is,
v(t) = v(max) sin ([tex]\sqrt{k/m}[/tex])t
v(max) = is the maximum velocity.
The kinetic energy is given as,
K(t) = 1/2 m[v(t)]²
Now, use the equation of position:
or, x(t) = A cos ([tex]\sqrt{k/m}[/tex])t
or, 0 = A cos ([tex]\sqrt{k/m}[/tex]) t₁
or, t₁ = π/2( [tex]\sqrt{k/m}[/tex])
Thus, the position of particle at time t₁ is 0. The cosine function is zero first time at angle π/2. The time can be calculated by substituting the values in the position function.
To know more about simple harmonic motion refer to:
https://brainly.com/question/20885248
#SPJ1
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