Simple harmonics ?? tough problem?

Question

A toy of mass 0.153 kg is undergoing SHM on the end of a horizontal spring with force constant k = 296 N/m. When the object is a distance 1.22×10^−2 m from its equilibrium position, it is observed to have a speed of 0.299 m/s.
SHM=simple harmonic motion
What is the total energy of the object at any point of its motion?

What is the amplitude of the motion?

What is the maximum speed attained by the object during its motion?

and the last two parts of the question, too confusing

Answer 1

Use the equation U = 0.5*k*x^2

U = potential energy (joules)
x = compression distance (meters)
k = force constant (N/m)

This gives us the potential energy of the toy.

U = 0.5 * 296 * 0.0122^2 = 0.0220 J

Then calculate the Kinetic Energy:

KE = 0.5 * m * V^2

KE = Kinetic Energy (joules)
m = Mass (kg)
V = Velocity (m/s)

KE = 0.5 * 0.153 * 0.299 = 0.0229 J

Total Energy = 0.0229 + 0.0220 = 0.0449 J

For part 2, assume total energy has been converted to potential energy and solve for compression distance:
x = sqrt (2 * U / k) = sqrt (2 * 0.0449 / 296) = 0.0174 m

Amplitude is twice the compression distance (for positive and negative)
Amplitude = 2 * 0.0174 = 0.0348 meters

For part 3, assume total energy has been converted to Kinetic energy and solve for speed:
V = sqrt (2 * KE / m) = sqrt (2 * 0.0449 / 0.153) = 0.766 m/s

Answer 2

b.) The equation for displacement is: x = A cos (wt + section) (the position A is the amplitude w is the angular frequency t is time) that's the equation stated on the starting up of the question, so A = 8.00, w = 4 and section = pi/6. The equation for speed is the by-product (calculus jargon) of the displacement equation with note of to time. From this, the speed equation seems to be: v = -Aw sin (wt + section) So at t = 0, speed = -32 sin pi/6 = -16 cm/s = 16 cm/s (provided that adverse skill no longer something the position vector parts like speed are worried) c.) The acceleration equation is the by-product of the speed equation with note of to time, so the acceleration equation is: a = -Aw^2 cos (wt + section) So at t = 0, acceleration = -128 cos pi/6 = 100 and ten.80 5 cm/s^2 = a million.1085 m/s^2 d.) Frequency = w / 2pi = 4 / 2pi = 0.6365 Hz era = a million / frequency = a million.571 s

Answer 3

Total Energy ===(k*(x.^2))/2 +1/2*m*(v.^2)

x= 1.22x10.^-2
v=0.299
m=0.153
k=296

substitute to calculate total energy ...


Now total energy is conserved....


===>1/2*k*(X.^2)=total energy ( calculated above)

X is the maximum displacement,here all the energy will be in the form of potential energy as kinetic energy would be xero

1/2* m * (V.^2)=TOTAL ENERGY


V is the maximum velocity which would be at the eqb position .P.E. ==0

Answer 4

E (energy) = M (mass)C(speed) squared