Can you please answer question 3.45 Integrative ActivitySimple Harmonic MotionThis small self-learning projectis a mandatory part of the course.Suppose we want to find a function y = f(t) such that its derivatives would satisfy the equationy"+o²y=0(DE)where a (a Greek lowercase letter called omega) is a positive constant. Such an equation involvinga function y = f(t) and its derivatives together is called a differential equation. Solving adifferential equation does not consist in finding a number that fits an equation, the goal is rather tofind a function that fits an equation. In the above, the goal is to find which function y = f(t)satisfies equation (DE).In general, finding functions that solve a differential equation is quite hard. We sometimes offera course on differential equations in your last term! For the specific differential equationy"+²y=0 that we have at hand, a solution is not too difficult. As you will verify below inquestion 3.41B, any function of the formy(t)= acos(at)+b sin(at)(GS1)where a and b are arbitrary constants, does satisfy differential equation (DE). Note thaty(t) = acos(at)+bsin(at) represents infinitely many possible functions due to the infinitelymany values that the arbitrary constants a and b can take. Moreover, it is shown in more advancedmathematics courses that there are no other possible functions satisfying equation (DE), that is,the infinitely many functions of equation (S1) give precisely all the possible functions that aresolutions of the differential equation (DE). We call (GS1) a general solution of (DE).With some trigonometry, it can be shown that another way to write the general solution of (DE) is(GS2)y(t) = Acos(at + p)where A and are constants and A is taken positive. As you will see in question 3.42 below, onemay switch between the two equivalent forms (GS1) and (GS2) of the general solution.There are many physical situations that lead to a differential equation such as (DE), called the(differential) equation of Simple Harmonic Motion; we will see one such example below. Asystem whose position as a function of time must satisfy the equation of Simple Harmonic Motion(DE), that is, whose position as a function of time will be given by a particular instance of equations(GS1) or (GS2), is said to undergo Simple Harmonic Motion. Note that in (GS2) corresponds toa "phase shift" (reason for the choice of the greak letter phi) compared to where the usual cosinefunction starts:dosePiftAmplitudeRTYTo aut Suppose now that a block of mass m is attached to one end of a horizontal spring, the other end ofwhich is fixed. Using Newton's F=ma and the fact that a is x", Hooke's Law becomes adifferential equation: mx"=-kox or x"=-x. The acceleration of the mass is proportional to thedisplacement from equilibrium. Putting =√k/m, we see that the system actually obeys thedifferential equation of Simple Harmonic Motion:x"+ @²x = 0.Thus Simple Harmonic Motion is obtained as the motion undergone by a particle under arestoring force proportional to the displacement (from an equilibrium point).The solution for the motion of the system is consequently already known as being of the form(GS1) or (GS2), taking@=Homework Question 3.45)Assume that the block has mass m = 0.2 kg and that the spring constant is k=57² kg/s². Supposenow that the block is pulled a distance of 2 cm from the equilibrium position of the spring andreleased from rest there at time t = 0.A) Find the position x(t) of the block at any time t.B) Give the amplitude, period, frequency and phase of the motion.Remarks: 1) The units for frequency are Hz or s¹, and the phase is an angle in radians (thus unitless).2) For part A), you can use form (GS1) or (GS2) of the solution. Often working with (GS1) is simplest, butwhen you are requested the phase, you may want to work directly with (GS2). Staring with (GS1) willrequire you to use conversions found in 3.42 to obtain the phase.sai 0

Name: Can you please answer question 3.45 Integrative ActivitySimple Harmoni
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Description: Can you please answer question 3.45 Integrative ActivitySimple Harmonic MotionThis small self-learning projectis a mandatory part of the course.Suppose we want to find a function y = f(t) such that its derivatives would satisfy the equationy"+o²y=0(D