Friday

October 31, 2014

October 31, 2014

Posted by **anon** on Friday, October 11, 2013 at 4:40am.

(1)What is the position of the block as a function of time. Express your answer in terms of t.

(2)How long will it take for the mass to first return to the equilibrium position?

(3)How long will it take for the spring to first become completely extended?

- physics -
**Elena**, Friday, October 11, 2013 at 2:32pmω₀=sqrt(k/m) = sqrt(20/6) =1.83 rad/s

T=2π/ ω =2π/1.83 =3.43 s.

(1)

x=Acos (ω₀t +α)

At t=0

-x₀=x

v₀=v(x)

v(x)= dx/dt = - ω₀Asin(ω₀t +α) … (1)

If t=0

-x₀=Acos (ω₀t +α) =Acosα…..(2)

and

v(x)= - ω₀Asin(ω₀t +α) =- ω₀Asin α…(3)

From (3)

Asin α =- v₀/ω₀ ……(4)

Divide (4) by (2)

Asin α/ Acosα = v₀/x₀•ω₀ =>

tan α= v₀/x₀•ω₀ = 5/1.7•1.83 =1.607

α=58° ≈1 rad

The square of (4) + the square of (2)

(Asin α)² +(Acosα)² =A²= (x₀)²+(v₀/ω₀)² =>

A=sqrt[(x₀)²+(v₀/ω₀)²] =

=sqrt{1.7² +(5/1.83)²}=3.22 m

The position of the object-spring system is given by

x(t) =3.22cos(1.83t+1) (m)

(2)

The spring first reaches equilibrium

at time t₁

x(t₁) = 0 =>

x(t₁) =3.22cos(1.83t₁+1) = 0

cos(1.83t₁+1)=0

1.83t₁+1 = π/2

t₁=[(π/2) -1)]/1.83=0.31 s.

(3)

The object is first completely extended when the velocity is zero.

v(x)= - ω₀Asin(ω₀t +α)=

=1.83•3.22sin(1.83t₂+1) =0,

sin(1.83t₂+1)=0

1.83t₂+1= π

t₂=(π-1)/1.83 =1.17 s.

**Answer this Question**

**Related Questions**

Physics Urgent please help - Consider an ideal spring that has an unstretched ...

Physics - Consider an ideal spring that has an unstretched length l0 = 3.9 m. ...

physics - Consider an ideal spring that has an unstretched length l0 = 3.9 m. ...

Physics - Consider an ideal spring that has an unstretched length l0 = 3.3 m. ...

physics - Consider an ideal spring that has an unstretched length l0 = 3.9 m. ...

Physics - Spring - Suppose a 1.5kg block of wood is slid along a floor and it ...

physics - Imagine a spring floating in space. This spring has a very small ...

Physics - An unstretched spring with spring constant 37 N/cm is suspended from ...

physic - Hooke's law describes a certain light spring of unstretched length 30.0...

PHYSICS - a 0.1 kg mass is suspended at rest from a spring near the Earth's ...