* Please write explanation and don't use calculatorConsider a damped spring-mass system with ? = 1kg, ? = 4 kg/s^2 and ? = 5 kg/s, driven by a sinusoidal forcing with ? = 2 rad/s.a. Write the equation of motion (the differential equation) for this systemb. Find the general solution_______________________________________________________________________?(?) = _____________________________________________________________________________________________ c. Solve the initial value problem if ?(0) = 1 and ?′(0) = 0?(?) = __________________________________________________________________________ ### Damped Spring-Mass System AnalysisThis section explores the dynamics of a damped spring-mass system subject to sinusoidal forcing. The system parameters include:- Mass ($ m $) = 1 kg- Spring constant ($ k $) = 4 kg/s²- Damping coefficient ($ b $) = 5 kg/s- Forcing frequency ($ \omega $) = 2 rad/s#### Tasks**a. Write the equation of motion (the differential equation) for this system.**The equation of motion incorporates the mass, damping, spring force, and the external forcing function. \[ \boxed{____________________________________________________________________________________________________________} \]**b. Find the general solution.**The general solution to the differential equation characterizes the system’s response over time.\[ y(t) = \boxed{____________________________________________________________________________________________________________} \]**c. Solve the initial value problem if $ y(0) = 1 $ and $ y'(0) = 0 $.**Solving the initial value problem applies specific initial conditions to determine a unique solution.\[ y(t) = \boxed{____________________________________________________________________________________________________________} \]This analysis is fundamental in studying oscillatory systems and understanding their behavior under various forces. The differential equations and their solutions provide insights into the system's transient and steady-state response.

Given m=1 kg,k=4 kg/s2,b=5 kg/s and ω=2rad/s

* Please write explanation and don't use calculator Consider a damped spring-mass system with ? = 1kg, ? = 4 kg/s^2 and ? = 5 kg/s, driven by a sinusoidal forcing with ? = 2 rad/s. a. Write the equation of motion (the differential equation) for this system b. Find the general solution _______________________________________________________________________ ?(?) = _____________________________________________________________________________________________ c. Solve the initial value problem if ?(0) = 1 and ?′(0) = 0 ?(?) = __________________________________________________________________________

* Please write explanation and don't use calculator Consider a damped spring-mass system with ? = 1kg, ? = 4 kg/s^2 and ? = 5 kg/s, driven by a sinusoidal forcing with ? = 2 rad/s. a. Write the equation of motion (the differential equation) for this system b. Find the general solution _________________________ ?(?) = _ c. Solve the initial value problem if ?(0) = 1 and ?′(0) = 0 ?(?) = ____________________________

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 74E

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