A mass undergoes simple harmonic motion with an amplitude of ( 10 mathrm{~cm} ). At the time considered as the beginning of time, its displacement is ( 0.05 mathrm{~m} ) and its velocity is ( -sqrt{3} mathrm{~m} / mathrm{s} ). (a) Determine the position of the object at a time of ( frac{pi}{5} mathrm{~s} ). (b) Determine the acceleration at ( t=0 mathrm{~s} ). (c) Graphically represent the magnitude of the restoring force as a function of distance, given that the mass of the object is ( 100 mathrm{~g} ).
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1 m). At the start (t = 0 s), the displacement is 0.05 m and the velocity is -√3 m/s. We need to find: (a) The position of the object at t = π/5 s. (b) The acceleration at t = 0 s. (c) Graph the magnitude of the restoring force as a function of distance. Show more…
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Harmonic Motion An object of mass $1 \mathrm{~kg}$ moves in simple harmonic motion, with an amplitude $A=0.24 \mathrm{~m}$ and a period of 4 seconds. The position $s$ of the object is given by $s(t)=A \cos (\omega t),$ where $t$ is the time in seconds. (a) Find the position of the object at time $t$ and at time $t=0.5$ seconds. (b) Find the velocity $v=v(t)$ of the object. (c) Find the velocity of the object when $t=0.5$ seconds. (d) Find the acceleration $a=a(t)$ of the object. (e) Use Newton's Second Law of Motion, $F=m a$, to find the magnitude and direction of the force acting on the object when $t=0.5$ second. (f) Find the minimum time required for the object to move from its initial position to the point where $s=-0.12 \mathrm{~m}$ (g) Find the velocity of the object when $s=-0.12 \mathrm{~m}$.
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A mass of 0.58 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.28 m)cos[(6 rad/s)t]. Determine the following. (a) Amplitude of oscillation for the oscillating mass (m) (b) Force constant for the spring (N/m) (c) Position of the mass after it has been oscillating for one half a period How long does it take the oscillating mass to travel from the maximum positive displacement to the maximum negative displacement? (m) (d) Position of the mass one-third of a period after it has been released How can you determine the position of the object at a specific time from an expression for the position of the object at any time? (m) (e) Time it takes the mass to get to the position x = -0.10 m after it has been released (s)
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