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LandOfStandar

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I now I have several threads but I need help with them all and thanks to who ever gives their time.

A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10.0N/m), and a damping force (F=-bv). Initially, it oscillates with and amplitude of 25.0cm; because of damping, the amplitude falls to three-fourths of this initial value at the completion of 4 oscillations.

a. what is the value of b?

b. how much energy has been lost during these four oscillations?

X(t) = Ae^(-bt/2m)

t = 4T

T = 2π(m/k)^(1/2)

E(t) = .5(k)(A^2)(e)^(-bt/m)

a. Can I assume damping does not affect the period of each oscillation.

t = 4T

T = 2π(m/k)^(1/2)

t = 4[2π(m/k)^(1/2)]

E(t) = .5(k)(A^2)(e)^(-bt/m)

(3/4)A = Ae^(-b(2π)(m/k)^(1/2)/2m) A are divided out

(3/4) = e^(-b(2π)(m/k)^(1/2)/2m)

In (3/4) = In e^(-b(2π)(m/k)^(1/2)/2m)

b = [(2m)In (3/4)]/[-b(2π)(m/k)^(1/2)]

= [(2x2.00kg)In (3/4)]/[-(2π)(2.00kg/10.N/m)^(1/2)]

= .102kg/s or 102g/s

b. Can I assume, once again, damping does not affect the period of each oscillation.

t = 4T

T = 2π(m/k)^(1/2)

t = 4[2π(m/k)^(1/2)]

E(t) = .5(k)(A^2)(e)^(-bt/m)

= .5(k)(A^2)(e)^(-b2π)(m/k)^(1/2)/m)

= .5(10.0n/m)(.250^2)(e)^(-.102kg/s2π)(2.00kg/10.0N/m)^(1/2)/2.00kg)

= .176KJ

Is my assumption wrong for this question?

## Homework Statement

A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10.0N/m), and a damping force (F=-bv). Initially, it oscillates with and amplitude of 25.0cm; because of damping, the amplitude falls to three-fourths of this initial value at the completion of 4 oscillations.

a. what is the value of b?

b. how much energy has been lost during these four oscillations?

## Homework Equations

X(t) = Ae^(-bt/2m)

t = 4T

T = 2π(m/k)^(1/2)

E(t) = .5(k)(A^2)(e)^(-bt/m)

## The Attempt at a Solution

a. Can I assume damping does not affect the period of each oscillation.

t = 4T

T = 2π(m/k)^(1/2)

t = 4[2π(m/k)^(1/2)]

E(t) = .5(k)(A^2)(e)^(-bt/m)

(3/4)A = Ae^(-b(2π)(m/k)^(1/2)/2m) A are divided out

(3/4) = e^(-b(2π)(m/k)^(1/2)/2m)

In (3/4) = In e^(-b(2π)(m/k)^(1/2)/2m)

b = [(2m)In (3/4)]/[-b(2π)(m/k)^(1/2)]

= [(2x2.00kg)In (3/4)]/[-(2π)(2.00kg/10.N/m)^(1/2)]

= .102kg/s or 102g/s

b. Can I assume, once again, damping does not affect the period of each oscillation.

t = 4T

T = 2π(m/k)^(1/2)

t = 4[2π(m/k)^(1/2)]

E(t) = .5(k)(A^2)(e)^(-bt/m)

= .5(k)(A^2)(e)^(-b2π)(m/k)^(1/2)/m)

= .5(10.0n/m)(.250^2)(e)^(-.102kg/s2π)(2.00kg/10.0N/m)^(1/2)/2.00kg)

= .176KJ

Is my assumption wrong for this question?

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