Problem 15.16 A 255 g mass attached to a horizontal spring oscillates at a frequ
ID: 1607510 • Letter: P
Question
Problem 15.16 A 255 g mass attached to a horizontal spring oscillates at a frequency of 3.10 Hz Att 0 s, the mass is at c 5.20 cm and has v 17.0 cm/s Determine: Part G The total energy Express your answer to three significant figures and include the appropriate units. 0.134 J Submit My Answers Give Up Correct Part H The position at t 0.400 s Express your answer to three significant figures and include the appropriate units. Value cm Submit My Answers Give Up incorrect, Try Again; 2 attempts remainingExplanation / Answer
here,
Max potential = kinetic + potential
0.5 * kA^2 = 0.5 * kx^2 + 0.5 * mv^2
kA^2 = kx^2 + mv^2
A^2 = x^2 + mv^2 / k
A^2 = x^2 + mv^2 / mw^2
A^2 = x^2 + ( v/w )^2
A^2 = ( 5.2 cm )^2 + ( - 17 cm/s / (2 * pi * 3.1) )^2
A = 5.27 cm
velocity = v(t)
v(t) = Aw·cos( wt + phi0 )
- 17 cm/s = ( 5.27 cm )( 2 * pi * 3.1 )cos( 0 + phi0 )
-0.166 = cos( phi0 )
phi0 = 1.4 radians
Position = s(t)
= A·sin[ wt + phi0 ]
= ( 5.27 cm )sin[ (2 * pi * 3.1)( 0.4 s ) + 1.4 ]
s(t) = 0.84 cm