Respuesta :
Answer:
x(t=1s) = -0.0125 m.
Explanation:
If the displacement as a function of time is given such that
[tex]x(t) = (0.074~{\rm m})\cos[(4.16~{\rm rad/s})t - 2.42~{\rm rad}]\\x(t = 1) = (0.074)\cos[4.16 - 2.42]\\x(t = 1) = (0.074)\cos[1.74]\\x(t = 1) = -0.0125~{\rm m}[/tex]
The characteristics of the simple harmonic movement allows to find the result for the displacement of the mass oscillated with the spring is:
x = 1.25 cm
Given parameters
- The mass is: m = 1.70 kg
- The displacement is: x = 7.40 cos (4.16t - 2.42)
To find
- The position at time t = 1.00 s
The simple harmonic movement is an oscillatory movement where the force is proportional to the displacement, this two by the expression
x = A cos (wt + Ф)
where x is the displacement, A the amplitude of the movement, w the angular velocity, t the time and Ф a phase constant determined by the initial conditions.
Indicates that the function of this simple harmonic motion is
x = 7.4 cos (4.16 t -2.42)
Remember that the angles must be in radians.
Let's calculate for the time of 1 s.
x = 7.4 cos (4.16 1 - 2.42)
x = 7.4 (- 0.1684)
x = -1.246 cm
The negative sign indicates that the spring is in the compression part.
In conclusion, using the characteristics of simple harmonic motion we can find the result for the displacement of the mass oscillated with the spring is:
x = 1.25 cm
Learn more here: brainly.com/question/17315536
