Construct a Table indicating the position x of the mass in Fig. 11–2 at times and where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?
FIGURE 11–2 Force on, and velocity of, a mass at different positions of its oscillation cycle on a frictionless surface.
FIGURE 11–8 Position as a function of time x = A cos(2πt/T).
FIGURE 11–9 Sinusoidal nature of SHM as a function of time; in this case, x = A sin(2πt/T) because at t = 0 the mass is at the equilibrium position x = 0, but it also has (or is given) an initial speed at t = 0 that carries it to x = A at
Solution Step 1 Listing the data Power required for an average human for the basic life processes = 100 W = 100 J/s Daily energy intake of a human, E = D 1 Day = 24 hours 1 Day = 24 × 60 minutes 4 1 Day = 24 × 60 × 60 seconds = 8.64×10 seconds 1 Cal = 1000 cal 1 Cal = 4184 joules Step 2 Mathematical calculations Power, P = Energy / time = E / t Therefore, Energy, E = P×t 4 Here, the daily energy intake of a human, E = 100D × 8.64 ×10 seconds 6 ED= 8.64 ×10 joules