Question

Se tiene un objeto que oscila con MAS. Si la amplitud del movimiento es de 15 cm y el periodo es de 2 seg, encontrar las magnitudes de la velocidad y la aceleración cuando: a) x= 0 cm b) x=7,5 cm Por favor, ayúdenme es para hoy :c

Answer 1

a) v = 0, a = - 15 pi²

b) v = - 40.8 cm / s, a = -74.2 cm / s

Step-by-step explanation:

the simple harmonic motion is described by the expression

x = A cos (wt + Ф)

in that case they indicate the amplitude of the movement

A = 15 cm

angular velocity and period are related

w = 2π / T

w = 2π/ 2

w = π rad / s

speed is defined by

v = dx / dt

v = -A w sin (wt + Ф)

acceleration is defined by

a = dv / dt

a = - A w² cos (wt + Ф)

In order to evaluate this expression we must know the value of the phase constant (Ф) that meets the initial conditions, the most common thing is that the system is released, v = 0 for y = 0 s, let's use the speed equation

v = -A w sin (0+ Ф)

for this expression to be zero, the sine must be zero, so

Ф= 0

now let's write the equations for our case

v = - 15 π sin (π t)

a = - 15 π² cos (π t)

a) for x = 0

v = 0

a = - 15 pi²

b) for x = 7.5 cm

Let's find out how long it takes to get to this position

x = 15 cos (π t)

7.5 / 15 = cos π t

pi t = cos⁻¹ 0.5

t = 1.047/π

don't forget that the angles are in radians

t = 0.333 s

now let's look for speed and acceleration

v = - 15 π sin (π 0.333)

v = - 40.8 cm / s

a = - 15 π² cos (π 0.333)

a = -74.2 cm / s