The 2.50 kg cube in the figure has edge lengths d = 6.50 cm and is mounted on an axle
through its center. a spring (k = 900 n/m) connects the cube's upper corner to a rigid wall.
initially the spring is at its rest length. if the cube is rotated 2.00° and released, what is the
period of the resulting shm?

The period of the resulting SHM is : 0.191 sec

Given data :

Edge length of cube = 6.50 cm

Spring ( K )  = 900 N/m  

Radius ( r ) =  

mass ( m ) = 2.50 kg

Determine the period of the resulting SHM

Distance stretched by the spring when the cube is stretched through θ =  r sin θ

Vertical distance from the center = r cos θ

F = k r sin θ

next step : determine the sum of torques

sum of torques ( ∑τ ) = I∝

                          F * r cos θ = I∝

                          ( k r sin θ ) r cos θ =  I∝  

                          k (d²/2) sin θ cos θ = I∝  ------ ( 1 )

Note : For cube rotating around its center I = 1/6 md²

Back to equation ( 1 )

k (d²/2) sin θ cos θ = 1/6 md² * ∝

k sin(2θ) = m∝     ( sin θ ≈ θ for small values like 2° )

∴ ∝ = ( 3k / m ) θ

d²θ/dt² = ( 3k / m ) θ

∴ Angular frequency ( w ) = √ (3k/m)

Final step : Calculate the value of the period of the resulting SHM

T = 2π / ω

  = 2π / √( m / (3k) )

  = 2π / √(2.50 kg / (3 * 900 N/m))

  = 0.191 sec

Learn more about oscillating Period : link

0.191 s

Explanation:

The distance from the center of the cube to the upper corner is r = d/√2.

When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ.  The new vertical distance from the center to the corner is r cos θ.

Sum of the torques:

∑τ = Iα

Fr cos θ = Iα

(k r sin θ) r cos θ = Iα

kr² sin θ cos θ = Iα

k (d²/2) sin θ cos θ = Iα

For a cube rotating about its center, I = ⅙ md².

k (d²/2) sin θ cos θ = ⅙ md² α

3k sin θ cos θ = mα

3/2 k sin(2θ) = mα

For small values of θ, sin θ ≈ θ.

3/2 k (2θ) = mα

α = (3k/m) θ

d²θ/dt² = (3k/m) θ

For this differential equation, the coefficient is the square of the angular frequency, ω².

ω² = 3k/m

ω = √(3k/m)

The period is:

T = 2π / ω

T = 2π √(m/(3k))

Given m = 2.50 kg and k = 900 N/m:

T = 2π √(2.50 kg / (3 × 900 N/m))

T = 0.191 s

The period is 0.191 seconds.

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation:

a.metals can become magnetic if they have many spinning electrons that create magnetic fields.d.only some metals are attracted by magnets; these metals are called ferromagnetic.

d.wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current.