### Problem 10-26: Spring-Mass System DisplacementThe displacement \( y(t) \) of a spring-mass system shown in Figure P10.26 is described by the differential equation:\[ 0.25 \, \ddot{y}(t) + 10 \, y(t) = 0. \]#### Tasks:(a) **Find the transient solution, \( y_{\text{tran}}(t) \).**(b) **Find the steady-state solution of the displacement, \( y_{\text{ss}} \).**(c) **Determine the total displacement \( y(t) \) given:**- Initial displacement \( y(0) = 0.2 \, \text{m} \)- Initial velocity \( \dot{y}(0) = 0 \, \text{m/s} \)(d) **Sketch the total displacement \( y(t) \).**#### Diagram Explanation:- The diagram illustrates a mass-spring system where a spring with stiffness \( k = 10 \, \text{N/m} \) is attached to a mass \( m = 0.25 \, \text{kg} \).- The system moves vertically with the displacement from the equilibrium position denoted as \( y(t) \).*Figure P10.26: Mass-spring system for Problem P10-26.*

Answered: Image /qna-images/answer/67a1b07a-39ea-4094-a6f6-7217d2546572.jpg

10-26. The displacement y(t) of a spring-mass system shown in Fig. P10.26 is given by 0.25 y(t) + 10 y(t) = 0. (a) Find the transient solution, yran(1). (b) Find the steady-state solution of the displacement yss (c) Determine the total displacement y(t) if the initial displacement y(0) = 0.2 m and the initial veloc- ity y(0) = 0 m/s. (d) Sketch the total displacement y(t). %3D %3D k= 10 N/m %3D 0.25 kg Figure P10.26 Mass-spring system for problem P10-26.

10-26. The displacement y(t) of a spring-mass system shown in Fig. P10.26 is given by 0.25 y(t) + 10 y(t) = 0. (a) Find the transient solution, yran(1). (b) Find the steady-state solution of the displacement yss (c) Determine the total displacement y(t) if the initial displacement y(0) = 0.2 m and the initial veloc- ity y(0) = 0 m/s. (d) Sketch the total displacement y(t). %3D %3D k= 10 N/m %3D 0.25 kg Figure P10.26 Mass-spring system for problem P10-26.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

### Problem 10-26: Spring-Mass System Displacement

The displacement \( y(t) \) of a spring-mass system shown in Figure P10.26 is described by the differential equation:

\[ 0.25 \, \ddot{y}(t) + 10 \, y(t) = 0. \]

#### Tasks:
(a) **Find the transient solution, \( y_{\text{tran}}(t) \).**

(b) **Find the steady-state solution of the displacement, \( y_{\text{ss}} \).**

(c) **Determine the total displacement \( y(t) \) given:**
- Initial displacement \( y(0) = 0.2 \, \text{m} \)
- Initial velocity \( \dot{y}(0) = 0 \, \text{m/s} \)

(d) **Sketch the total displacement \( y(t) \).**

#### Diagram Explanation:
- The diagram illustrates a mass-spring system where a spring with stiffness \( k = 10 \, \text{N/m} \) is attached to a mass \( m = 0.25 \, \text{kg} \).
- The system moves vertically with the displacement from the equilibrium position denoted as \( y(t) \).

*Figure P10.26: Mass-spring system for Problem P10-26.*

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