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At the initial moment a particle's displacement is 4.3 cm and its velocity is -3.2 m/s. The particle's mass is 4 kg and its total energy 79.5 J Write down the equation. Here and below the units used are the SI units, i.e. the displacement amplitude is expressed in meters, the time in seconds, the frequency in hertz, the phase in radians. of the vibrations and find the distance travelled by the particle in 0.4 s. |
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Answer» `s_(0)=Acosvarphi,v_(v)-Aomegasinvarphi, Wmomega^(2)A^(2)//2` giving `sinvarphi=-(v_(0))/(Aomega)=-v_(0)sqrt((m)/(2W))` Since `sinvarphigt0` and `cosvarphigt0`, it follows that the initial phase `varphi` lies in the INTERVAL `0ltvarphiltpi//2`. The circular frequency is `omega=-(v_(0))/(s_(0))cotvarphi`, the amplitude A `=sqrt(s_(0)^(2)+((v_(0))/(w))^a)`. The period of oscillations is 50 ms, so the time of 0.4 s spans 8 periods. During this time the particle will cover a distance equal to 32 amplitudes. |
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