A mass on a spring vibrates in simple harmonic motion at a frequency of 6 Hz and

Question

A mass on a spring vibrates in simple harmonic motion at a frequency of 6 Hz and an amplitude of 7 cm. If a timer is started when its displacement is a maximum (hence x = 7 cm when t = 0), what is the displacement of the mass when t = 2.4 s? -5.663 cm -17.5 cm 12.6 cm 4 cm 4.32 cm A 34 gm cube of ice, initially at 0 degree C is dropped into 220 gm of water in a 110 gm aluminum container, both initilly at 25 degree C. What is the final equilibrium temperature? (Specific heat for aluminum is 0.215 cal/gm-C degree and L_f = 80 cal/gm.) 13.84 degree C 5.3856 degree C 11.333333 degree C 24 degree C 14.45 degree C

Explanation / Answer

19

SInce it is SHM

Equation of SHM is

x=Acos(wt)

A=7 cm

w=2*pi*6=37.7 rad/s

x=7cos(37.7t)

at t=2.4 sec

we got

x=-5.663 cm

so (A) is correct

20

let the final tem is T

Heat lost =heat gained

34*80 +34*T=220*1*(25-T) + (110*0.215*(25-T)

we got T=12.14 C

None of the answer is correct

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