Question

MY NOTES

A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 12 cm above the ground and released. After that, it bounces up and down between its minimum height of 12 cm and a maximum height of 22 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 0.8 seconds after starting.

(b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean 17 amplitude 5 phase shift period (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) (d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the equation shown below. h(t) = A sin ( 274 (4 - c)); + D h(t) = X (e) What is the height of the weight after 2.4 seconds? cm (f) During the first 10 seconds, how many times will the weight be exactly 19 cm above the floor? (Note: This problem does not require inverse trigonometry.)

Answer 1

PANKA Date Page No. Y = +A ~ Amplitude ftur Mean position y=0) 12et) Love y-- [At tao bay = 20 (mm 170m hmin = 12cm ground
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Here २7 - 2 1.6 PANKAN Date A = 5cm Page No. Ih(t) 17+ si sin (27 f - Mg) cm ooy) in h(t) = 17+ ssin at To6 Oy At 9.4 second h(t) = 1 + s 2 ( 2-4 - 04) het 17 +5X1 22cm f time Periode 1.6 sec Hence ho. cycle me to go Here can see in = 60.25 h=64 that ponticle Complete 7th cycles Yy complete particle's position 10 sec & cycles and particle h, 11cm) After Weight exactly exatimes 19 times 19 Cm above floor