An object attached to a spring undergoes simple harmonic motion modeled by the differential equationd²x=0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is themass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters.dt²Use this information to find the spring constant. (Use g = 9.8 meters/second²)mk=+ kxThe previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass isdisplaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second.Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constantsin your equation.x(t) =Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leaveunknown constants in your equation.x(t) =

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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An object attached to a spring undergoes simple harmonic motion modeled by the differential equation
d²x
=
0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the
mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters.
dt²
Use this information to find the spring constant. (Use g = 9.8 meters/second²)
m
k
=
+ kx
The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is
displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second.
Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants
in your equation.
x(t) =
Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave
unknown constants in your equation.
x(t) =

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Step 1: Given

$SHM space differential space equation space straight m fraction numerator straight d squared straight x over denominator dt squared end fraction plus kx equals 0 when space straight m subscript 1 equals 3 space kg space increment straight l equals 0.2 space straight m straight g equals 9.8 space straight m divided by straight s squared part space 1 space find space straight k equals ? part space 2 when space straight m equals 17 space kg space space straight x open parentheses straight t equals 0 close parentheses equals 0.45 straight m space space straight V subscript 1 equals 2 space straight m divided by straight s straight x open parentheses straight t close parentheses equals straight c subscript 1 cos open parentheses straight omega straight t close parentheses plus straight c subscript 2 sin open parentheses straight omega straight t close parentheses part space 3 straight x open parentheses straight t close parentheses equals Asin open parentheses straight omega straight t plus straight ϕ close parentheses space space where space 0 less or equal than straight ϕ less than 2 straight pi$

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