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The result of the interpolated motion function is plotted in Fig 534 As mentioned, should the constraint data array be incomplete, the methods described earlier could be used to ll in the gaps For example, had the data table been incomplete, as in Table 59, the missing points could be supplied by interpolating along the rows and columns The results of doing so appear in Tables 510 and 511

t ln(3/5) 100

Although locking a method s code, as shown in the previous example, is an easy and effective means of achieving synchronization, it will not work in all cases For example, you might want to synchronize access to a method of a class you did not create, which is itself not synchronized This can occur if you want to use a class that was written by a third party and for which you do not have access to the source code Thus, it is not possible for you to add a lock statement to the appropriate method within the class How can access to an object of this class be synchronized Fortunately, the solution to this problem is simple: Lock access to the object from code outside the object by specifying the object in a lock statement For example, here is an alternative implementation of the preceding program Notice that the code within SumIt( ) is no longer locked and no longer declares the lockOn object Instead, calls to SumIt( ) are locked within MyThread

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// Another way to use lock to synchronize access to an object using System; using SystemThreading; class SumArray { int sum; public int SumIt(int[] nums) { sum = 0; // reset sum for(int i=0; i < numsLength; i++) { sum += nums[i]; ConsoleWriteLine("Running total for " + ThreadCurrentThreadName + " is " + sum); ThreadSleep(10); // allow task-switch } return sum;

Cam translation s2 (mm) 0 0 0 0 0 0 0 0 50 0 003 0053 061 050 007 0 120 0 020 353 403 331 050 0

Part II:

We conclude that there is 1 gram of radioactive material remaining when t = 100 ln(1/5) 315066 ln(3/5)

} } class MyThread { public Thread Thrd; int[] a; int answer; /* Create one SumArray object for all instances of MyThread */ static SumArray sa = new SumArray(); // Construct a new thread public MyThread(string name, int[] nums) { a = nums; Thrd = new Thread(thisRun); ThrdName = name; ThrdStart(); // start the thread } // Begin execution of new thread void Run() { ConsoleWriteLine(ThrdName + " starting"); // Lock calls to SumIt() lock(sa) answer = saSumIt(a); ConsoleWriteLine("Sum for " + ThrdName + " is " + answer); ConsoleWriteLine(ThrdName + " terminating"); } } class Sync { static void Main() { int[] a = {1, 2, 3, 4, 5}; MyThread mt1 = new MyThread("Child #1", a); MyThread mt2 = new MyThread("Child #2", a); mt1ThrdJoin(); mt2ThrdJoin(); } }

Cam rotation f2 (deg) 180 0 024 438 500 412 062 00 235 0 021 370 422 348 052 0 315 0 002 040 045 037 006 0 360 0 0 0 0 0 0 0

Here, the call to saSumIt( ) is locked, rather than the code inside SumIt( ) itself The code that accomplishes this is shown here:

// Lock calls to SumIt() lock(sa) answer = saSumIt(a);

0 5 18 25 33 43 50

So at time t = 315066, or after 215066 more years, there will be 1 gram of the isotope remaining You Try It: Our analysis of exponential growth and decay is derived from the hypothesis that the rate of growth is proportional to the amount of matter present Suppose instead that we are studying a system in which the rate of decay is proportional to the square of the amount of matter Let M(t) denote the amount of matter at time t Then our physical law is expressed as dM = C M 2 dt

Because sa is a private object, it is safe to lock on Using this approach, the program produces the same correct results as the original approach

23:

Cam translation s2 (mm) 0 0 0 0 0 0 0 0 50 0 003 053 061 050 007 0 120 0 020 403 331 0

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