Answer:
y = -19.2 sin (23.15t) cm
Explanation:
The spring mass system is an oscillatory movement that is described by the equation
y = yo cos (wt + φ)
Let's look for the terms of this equation the amplitude I
y₀ = 19.2 cm
Angular velocity is
w = √ (k / m)
w = √ (245 / 0.457
w = 23.15 rad / s
The φ phase is determined for the initial condition t = 0 s
, the velocity is negative v (0) = -vo
The speed of the equation is obtained by the derivative with respect to time
v = dy / dt
v = - y₀ w sin (wt + φ)
For t = 0
-vo = -yo w sin φ
The angular and linear velocity are related v = w r
v₀ = w r₀
v₀ = v₀ sinφ
sinφ = 1
φ = sin⁻¹ 1
φ = π / 4 rad
Let's build the equation
y = 19.2 cos (23.15 t + π/ 4)
Let's use the trigonometric ratio π/ 4 = 90º
Cos (a +90) = cos a cos90 - sin a sin sin 90 = 0 - sin a
y = -19.2 sin (23.15t) cm
Answer:
10.3 cm³
Explanation:
From the question given above, the following data were obtained:
Original volume (V₁) = 10 cm³
Initial temperature (θ₁) = 20 °C
Final temperature (θ₂) = 50 °C
Cubic expansivity (γ) = 10¯³ K¯¹
Final volume (V₂) =?
γ = V₂ – V₁ / V₁(θ₂ – θ₁)
10¯³ = V₂ – 10 / 10( 50 – 20)
10¯³ = V₂ – 10 / 10(30)
10¯³ = V₂ – 10 / 300
Cross multiply
10¯³ × 300 = V₂ – 10
0.3 = V₂ – 10
Collect like terms
0.3 + 10 = V₂
10.3 = V₂
V₂ = 10.3 cm³
Thus, the volume at 50 °C is 10.3 cm³
Answer: JOB
Explanation: They full forms of work are JOB which is JUST OBEY BOSS or Joining Other Bussiness .
